id	sid	tid	token	lemma	pos
ap-6836	1	1	acta	acta	PROPN
ap-6836	1	2	polytechnica	polytechnica	PROPN
ap-6836	1	3	https://doi.org/10.14311/ap.2021.61.0428	https://doi.org/10.14311/ap.2021.61.0428	VERB
ap-6836	1	4	acta	acta	PROPN
ap-6836	1	5	polytechnica	polytechnica	PROPN
ap-6836	1	6	61(3):428–434	61(3):428–434	PROPN
ap-6836	1	7	,	,	PUNCT
ap-6836	1	8	2021	2021	NUM
ap-6836	1	9	©	©	ADP
ap-6836	1	10	2021	2021	NUM
ap-6836	1	11	the	the	DET
ap-6836	1	12	author(s	author(s	NOUN
ap-6836	1	13	)	)	PUNCT
ap-6836	1	14	.	.	PUNCT
ap-6836	2	1	licensed	license	VERB
ap-6836	2	2	under	under	ADP
ap-6836	2	3	a	a	DET
ap-6836	2	4	cc	cc	NOUN
ap-6836	2	5	-	-	PUNCT
ap-6836	2	6	by	by	ADP
ap-6836	2	7	4.0	4.0	NUM
ap-6836	2	8	licence	licence	NOUN
ap-6836	2	9	published	publish	VERB
ap-6836	2	10	by	by	ADP
ap-6836	2	11	the	the	DET
ap-6836	2	12	czech	czech	PROPN
ap-6836	2	13	technical	technical	PROPN
ap-6836	2	14	university	university	PROPN
ap-6836	2	15	in	in	ADP
ap-6836	2	16	prague	prague	PROPN
ap-6836	2	17	antipalindromic	antipalindromic	ADJ
ap-6836	2	18	numbers	number	NOUN
ap-6836	2	19	ľubomíra	ľubomíra	ADJ
ap-6836	2	20	dvořákováa,∗	dvořákováa,∗	PROPN
ap-6836	2	21	,	,	PUNCT
ap-6836	2	22	stanislav	stanislav	NOUN
ap-6836	2	23	krumla	krumla	NOUN
ap-6836	2	24	,	,	PUNCT
ap-6836	2	25	david	david	PROPN
ap-6836	2	26	ryzákb	ryzákb	PROPN
ap-6836	2	27	a	a	DET
ap-6836	2	28	czech	czech	PROPN
ap-6836	2	29	technical	technical	PROPN
ap-6836	2	30	university	university	PROPN
ap-6836	2	31	in	in	ADP
ap-6836	2	32	prague	prague	PROPN
ap-6836	2	33	,	,	PUNCT
ap-6836	2	34	faculty	faculty	NOUN
ap-6836	2	35	of	of	ADP
ap-6836	2	36	nuclear	nuclear	ADJ
ap-6836	2	37	sciences	science	NOUN
ap-6836	2	38	and	and	CCONJ
ap-6836	2	39	physical	physical	ADJ
ap-6836	2	40	engineering	engineering	NOUN
ap-6836	2	41	,	,	PUNCT
ap-6836	2	42	department	department	NOUN
ap-6836	2	43	of	of	ADP
ap-6836	2	44	mathematics	mathematic	NOUN
ap-6836	2	45	,	,	PUNCT
ap-6836	2	46	trojanova	trojanova	X
ap-6836	2	47	13	13	NUM
ap-6836	2	48	,	,	PUNCT
ap-6836	2	49	120	120	NUM
ap-6836	2	50	00	00	NUM
ap-6836	2	51	praha	praha	PROPN
ap-6836	2	52	2	2	NUM
ap-6836	2	53	,	,	PUNCT
ap-6836	2	54	czech	czech	PROPN
ap-6836	2	55	republic	republic	PROPN
ap-6836	2	56	b	b	PROPN
ap-6836	2	57	charles	charles	PROPN
ap-6836	2	58	university	university	PROPN
ap-6836	2	59	,	,	PUNCT
ap-6836	2	60	faculty	faculty	NOUN
ap-6836	2	61	of	of	ADP
ap-6836	2	62	mathematics	mathematic	NOUN
ap-6836	2	63	and	and	CCONJ
ap-6836	2	64	physics	physics	PROPN
ap-6836	2	65	,	,	PUNCT
ap-6836	2	66	ke	ke	PROPN
ap-6836	2	67	karlovu	karlovu	PROPN
ap-6836	2	68	2027	2027	NUM
ap-6836	2	69	,	,	PUNCT
ap-6836	2	70	121	121	NUM
ap-6836	2	71	16	16	NUM
ap-6836	2	72	praha	praha	NOUN
ap-6836	2	73	2	2	NUM
ap-6836	2	74	,	,	PUNCT
ap-6836	2	75	czech	czech	PROPN
ap-6836	2	76	republic	republic	NOUN
ap-6836	2	77	∗	∗	NOUN
ap-6836	2	78	corresponding	correspond	VERB
ap-6836	2	79	author	author	NOUN
ap-6836	2	80	:	:	PUNCT
ap-6836	2	81	lubomira.dvorakova@fjfi.cvut.cz	lubomira.dvorakova@fjfi.cvut.cz	ADJ
ap-6836	2	82	abstract	abstract	ADJ
ap-6836	2	83	.	.	PUNCT
ap-6836	3	1	everybody	everybody	PRON
ap-6836	3	2	has	have	AUX
ap-6836	3	3	certainly	certainly	ADV
ap-6836	3	4	heard	hear	VERB
ap-6836	3	5	about	about	ADP
ap-6836	3	6	palindromes	palindrome	NOUN
ap-6836	3	7	:	:	PUNCT
ap-6836	3	8	words	word	NOUN
ap-6836	3	9	that	that	PRON
ap-6836	3	10	stay	stay	VERB
ap-6836	3	11	the	the	DET
ap-6836	3	12	same	same	ADJ
ap-6836	3	13	when	when	SCONJ
ap-6836	3	14	read	read	VERB
ap-6836	3	15	backwards	backwards	ADV
ap-6836	3	16	.	.	PUNCT
ap-6836	4	1	for	for	ADP
ap-6836	4	2	instance	instance	NOUN
ap-6836	4	3	,	,	PUNCT
ap-6836	4	4	kayak	kayak	NOUN
ap-6836	4	5	,	,	PUNCT
ap-6836	4	6	radar	radar	NOUN
ap-6836	4	7	,	,	PUNCT
ap-6836	4	8	or	or	CCONJ
ap-6836	4	9	rotor	rotor	NOUN
ap-6836	4	10	.	.	PUNCT
ap-6836	4	11	mathematicians	mathematician	NOUN
ap-6836	4	12	are	be	AUX
ap-6836	4	13	interested	interested	ADJ
ap-6836	4	14	in	in	ADP
ap-6836	4	15	palindromic	palindromic	ADJ
ap-6836	4	16	numbers	number	NOUN
ap-6836	4	17	:	:	PUNCT
ap-6836	4	18	positive	positive	ADJ
ap-6836	4	19	integers	integer	NOUN
ap-6836	4	20	whose	whose	DET
ap-6836	4	21	expansion	expansion	NOUN
ap-6836	4	22	in	in	ADP
ap-6836	4	23	a	a	DET
ap-6836	4	24	certain	certain	ADJ
ap-6836	4	25	integer	integer	NOUN
ap-6836	4	26	base	base	NOUN
ap-6836	4	27	is	be	AUX
ap-6836	4	28	a	a	DET
ap-6836	4	29	palindrome	palindrome	NOUN
ap-6836	4	30	.	.	PUNCT
ap-6836	5	1	the	the	DET
ap-6836	5	2	following	follow	VERB
ap-6836	5	3	problems	problem	NOUN
ap-6836	5	4	are	be	AUX
ap-6836	5	5	studied	study	VERB
ap-6836	5	6	:	:	PUNCT
ap-6836	5	7	palindromic	palindromic	ADJ
ap-6836	5	8	primes	prime	NOUN
ap-6836	5	9	,	,	PUNCT
ap-6836	5	10	palindromic	palindromic	ADJ
ap-6836	5	11	squares	square	NOUN
ap-6836	5	12	and	and	CCONJ
ap-6836	5	13	higher	high	ADJ
ap-6836	5	14	powers	power	NOUN
ap-6836	5	15	,	,	PUNCT
ap-6836	5	16	multi	multi	ADJ
ap-6836	5	17	-	-	ADJ
ap-6836	5	18	base	base	ADJ
ap-6836	5	19	palindromic	palindromic	ADJ
ap-6836	5	20	numbers	number	NOUN
ap-6836	5	21	,	,	PUNCT
ap-6836	5	22	etc	etc	X
ap-6836	5	23	.	.	X
ap-6836	6	1	in	in	ADP
ap-6836	6	2	this	this	DET
ap-6836	6	3	paper	paper	NOUN
ap-6836	6	4	,	,	PUNCT
ap-6836	6	5	we	we	PRON
ap-6836	6	6	define	define	VERB
ap-6836	6	7	and	and	CCONJ
ap-6836	6	8	study	study	VERB
ap-6836	6	9	antipalindromic	antipalindromic	ADJ
ap-6836	6	10	numbers	number	NOUN
ap-6836	6	11	:	:	PUNCT
ap-6836	6	12	positive	positive	ADJ
ap-6836	6	13	integers	integer	NOUN
ap-6836	6	14	whose	whose	DET
ap-6836	6	15	expansion	expansion	NOUN
ap-6836	6	16	in	in	ADP
ap-6836	6	17	a	a	DET
ap-6836	6	18	certain	certain	ADJ
ap-6836	6	19	integer	integer	NOUN
ap-6836	6	20	base	base	NOUN
ap-6836	6	21	is	be	AUX
ap-6836	6	22	an	an	DET
ap-6836	6	23	antipalindrome	antipalindrome	ADJ
ap-6836	6	24	.	.	PUNCT
ap-6836	7	1	we	we	PRON
ap-6836	7	2	present	present	VERB
ap-6836	7	3	new	new	ADJ
ap-6836	7	4	results	result	NOUN
ap-6836	7	5	concerning	concern	VERB
ap-6836	7	6	divisibility	divisibility	NOUN
ap-6836	7	7	and	and	CCONJ
ap-6836	7	8	antipalindromic	antipalindromic	ADJ
ap-6836	7	9	primes	prime	NOUN
ap-6836	7	10	,	,	PUNCT
ap-6836	7	11	antipalindromic	antipalindromic	ADJ
ap-6836	7	12	squares	square	NOUN
ap-6836	7	13	and	and	CCONJ
ap-6836	7	14	higher	high	ADJ
ap-6836	7	15	powers	power	NOUN
ap-6836	7	16	,	,	PUNCT
ap-6836	7	17	and	and	CCONJ
ap-6836	7	18	multi	multi	ADJ
ap-6836	7	19	-	-	ADJ
ap-6836	7	20	base	base	ADJ
ap-6836	7	21	antipalindromic	antipalindromic	ADJ
ap-6836	7	22	numbers	number	NOUN
ap-6836	7	23	.	.	PUNCT
ap-6836	8	1	we	we	PRON
ap-6836	8	2	provide	provide	VERB
ap-6836	8	3	a	a	DET
ap-6836	8	4	user	user	NOUN
ap-6836	8	5	-	-	PUNCT
ap-6836	8	6	friendly	friendly	ADJ
ap-6836	8	7	application	application	NOUN
ap-6836	8	8	for	for	ADP
ap-6836	8	9	all	all	DET
ap-6836	8	10	studied	studied	ADJ
ap-6836	8	11	questions	question	NOUN
ap-6836	8	12	.	.	PUNCT
ap-6836	9	1	keywords	keyword	NOUN
ap-6836	9	2	:	:	PUNCT
ap-6836	9	3	expansion	expansion	NOUN
ap-6836	9	4	in	in	ADP
ap-6836	9	5	a	a	DET
ap-6836	9	6	base	base	NOUN
ap-6836	9	7	,	,	PUNCT
ap-6836	9	8	palindromes	palindrome	NOUN
ap-6836	9	9	,	,	PUNCT
ap-6836	9	10	antipalindromes	antipalindrome	NOUN
ap-6836	9	11	,	,	PUNCT
ap-6836	9	12	palindromic	palindromic	ADJ
ap-6836	9	13	numbers	number	NOUN
ap-6836	9	14	,	,	PUNCT
ap-6836	9	15	antipalindromic	antipalindromic	ADJ
ap-6836	9	16	numbers	number	NOUN
ap-6836	9	17	.	.	PUNCT
ap-6836	10	1	1	1	X
ap-6836	10	2	.	.	X
ap-6836	10	3	introduction	introduction	NOUN
ap-6836	10	4	everybody	everybody	PRON
ap-6836	10	5	has	have	AUX
ap-6836	10	6	certainly	certainly	ADV
ap-6836	10	7	heard	hear	VERB
ap-6836	10	8	about	about	ADP
ap-6836	10	9	palindromes	palindrome	NOUN
ap-6836	10	10	:	:	PUNCT
ap-6836	10	11	words	word	NOUN
ap-6836	10	12	that	that	PRON
ap-6836	10	13	stay	stay	VERB
ap-6836	10	14	the	the	DET
ap-6836	10	15	same	same	ADJ
ap-6836	10	16	when	when	SCONJ
ap-6836	10	17	read	read	VERB
ap-6836	10	18	backwards	backwards	ADV
ap-6836	10	19	.	.	PUNCT
ap-6836	11	1	for	for	ADP
ap-6836	11	2	instance	instance	NOUN
ap-6836	11	3	,	,	PUNCT
ap-6836	11	4	kayak	kayak	NOUN
ap-6836	11	5	,	,	PUNCT
ap-6836	11	6	radar	radar	NOUN
ap-6836	11	7	,	,	PUNCT
ap-6836	11	8	or	or	CCONJ
ap-6836	11	9	rotor	rotor	NOUN
ap-6836	11	10	.	.	PUNCT
ap-6836	12	1	it	it	PRON
ap-6836	12	2	is	be	AUX
ap-6836	12	3	not	not	PART
ap-6836	12	4	surprising	surprising	ADJ
ap-6836	12	5	that	that	SCONJ
ap-6836	12	6	in	in	ADP
ap-6836	12	7	natural	natural	ADJ
ap-6836	12	8	languages	language	NOUN
ap-6836	12	9	,	,	PUNCT
ap-6836	12	10	it	it	PRON
ap-6836	12	11	is	be	AUX
ap-6836	12	12	impossible	impossible	ADJ
ap-6836	12	13	to	to	PART
ap-6836	12	14	find	find	VERB
ap-6836	12	15	extremely	extremely	ADV
ap-6836	12	16	long	long	ADJ
ap-6836	12	17	palindromes	palindrome	NOUN
ap-6836	12	18	.	.	PUNCT
ap-6836	13	1	the	the	DET
ap-6836	13	2	longest	long	ADJ
ap-6836	13	3	palindrome	palindrome	NOUN
ap-6836	13	4	in	in	ADP
ap-6836	13	5	english	english	PROPN
ap-6836	13	6	is	be	AUX
ap-6836	13	7	“	"	PUNCT
ap-6836	13	8	tattarrattat	tattarrattat	PROPN
ap-6836	13	9	”	"	PUNCT
ap-6836	13	10	.	.	PUNCT
ap-6836	14	1	however	however	ADV
ap-6836	14	2	its	its	PRON
ap-6836	14	3	victory	victory	NOUN
ap-6836	14	4	is	be	AUX
ap-6836	14	5	doubtful	doubtful	ADJ
ap-6836	14	6	since	since	SCONJ
ap-6836	14	7	tattarrattat	tattarrattat	NOUN
ap-6836	14	8	is	be	AUX
ap-6836	14	9	a	a	DET
ap-6836	14	10	neologism	neologism	NOUN
ap-6836	14	11	created	create	VERB
ap-6836	14	12	by	by	ADP
ap-6836	14	13	james	james	PROPN
ap-6836	14	14	joyce	joyce	PROPN
ap-6836	14	15	in	in	ADP
ap-6836	14	16	his	his	PRON
ap-6836	14	17	novel	novel	NOUN
ap-6836	14	18	ulysses	ulysse	NOUN
ap-6836	15	1	[	[	X
ap-6836	15	2	1	1	NUM
ap-6836	15	3	]	]	PUNCT
ap-6836	15	4	;	;	PUNCT
ap-6836	15	5	it	it	PRON
ap-6836	15	6	expresses	express	VERB
ap-6836	15	7	loud	loud	ADJ
ap-6836	15	8	knocking	knock	VERB
ap-6836	15	9	at	at	ADP
ap-6836	15	10	the	the	DET
ap-6836	15	11	door	door	NOUN
ap-6836	15	12	:	:	PUNCT
ap-6836	15	13	“	"	PUNCT
ap-6836	15	14	i	i	PRON
ap-6836	15	15	was	be	AUX
ap-6836	15	16	just	just	ADV
ap-6836	15	17	beginning	begin	VERB
ap-6836	15	18	to	to	ADP
ap-6836	15	19	yawn	yawn	NOUN
ap-6836	15	20	with	with	ADP
ap-6836	15	21	nerves	nerve	NOUN
ap-6836	15	22	thinking	think	VERB
ap-6836	15	23	he	he	PRON
ap-6836	15	24	was	be	AUX
ap-6836	15	25	trying	try	VERB
ap-6836	15	26	to	to	PART
ap-6836	15	27	make	make	VERB
ap-6836	15	28	a	a	DET
ap-6836	15	29	fool	fool	NOUN
ap-6836	15	30	of	of	ADP
ap-6836	15	31	me	i	PRON
ap-6836	15	32	when	when	SCONJ
ap-6836	15	33	i	i	PRON
ap-6836	15	34	knew	know	VERB
ap-6836	15	35	his	his	PRON
ap-6836	15	36	tattarrattat	tattarrattat	NOUN
ap-6836	15	37	at	at	ADP
ap-6836	15	38	the	the	DET
ap-6836	15	39	door	door	NOUN
ap-6836	15	40	.	.	PUNCT
ap-6836	15	41	”	"	PUNCT
ap-6836	16	1	palindromic	palindromic	ADJ
ap-6836	16	2	phrases	phrase	NOUN
ap-6836	16	3	are	be	AUX
ap-6836	16	4	even	even	ADV
ap-6836	16	5	more	more	ADV
ap-6836	16	6	interesting	interesting	ADJ
ap-6836	16	7	.	.	PUNCT
ap-6836	17	1	they	they	PRON
ap-6836	17	2	provide	provide	VERB
ap-6836	17	3	palindromes	palindrome	NOUN
ap-6836	17	4	if	if	SCONJ
ap-6836	17	5	punctuation	punctuation	NOUN
ap-6836	17	6	,	,	PUNCT
ap-6836	17	7	capitalization	capitalization	NOUN
ap-6836	17	8	,	,	PUNCT
ap-6836	17	9	and	and	CCONJ
ap-6836	17	10	spaces	space	NOUN
ap-6836	17	11	are	be	AUX
ap-6836	17	12	ignored	ignore	VERB
ap-6836	17	13	.	.	PUNCT
ap-6836	18	1	some	some	DET
ap-6836	18	2	popular	popular	ADJ
ap-6836	18	3	palindromic	palindromic	ADJ
ap-6836	18	4	phrases	phrase	NOUN
ap-6836	18	5	(	(	PUNCT
ap-6836	18	6	the	the	DET
ap-6836	18	7	last	last	ADJ
ap-6836	18	8	one	one	NUM
ap-6836	18	9	devoted	devote	VERB
ap-6836	18	10	to	to	ADP
ap-6836	18	11	mathematicians	mathematician	NOUN
ap-6836	18	12	)	)	PUNCT
ap-6836	18	13	in	in	ADP
ap-6836	18	14	english	english	PROPN
ap-6836	18	15	are	be	AUX
ap-6836	18	16	:	:	PUNCT
ap-6836	18	17	“	"	PUNCT
ap-6836	18	18	do	do	AUX
ap-6836	18	19	geese	geese	NOUN
ap-6836	18	20	see	see	VERB
ap-6836	18	21	god	god	PROPN
ap-6836	18	22	?	?	PUNCT
ap-6836	18	23	”	"	PUNCT
ap-6836	19	1	“	"	PUNCT
ap-6836	19	2	a	a	DET
ap-6836	19	3	man	man	NOUN
ap-6836	19	4	,	,	PUNCT
ap-6836	19	5	a	a	DET
ap-6836	19	6	plan	plan	NOUN
ap-6836	19	7	,	,	PUNCT
ap-6836	19	8	a	a	DET
ap-6836	19	9	canal	canal	NOUN
ap-6836	19	10	:	:	PUNCT
ap-6836	19	11	panama	panama	PROPN
ap-6836	19	12	.	.	PUNCT
ap-6836	19	13	”	"	PUNCT
ap-6836	20	1	“	"	PUNCT
ap-6836	20	2	madam	madam	NOUN
ap-6836	20	3	,	,	PUNCT
ap-6836	20	4	in	in	ADP
ap-6836	20	5	eden	eden	PROPN
ap-6836	20	6	,	,	PUNCT
ap-6836	20	7	i	i	PRON
ap-6836	20	8	’m	’m	VERB
ap-6836	20	9	adam	adam	PROPN
ap-6836	20	10	.	.	PUNCT
ap-6836	20	11	”	"	PUNCT
ap-6836	21	1	“	"	PUNCT
ap-6836	21	2	never	never	ADV
ap-6836	21	3	odd	odd	ADJ
ap-6836	21	4	or	or	CCONJ
ap-6836	21	5	even	even	ADV
ap-6836	21	6	”	"	PUNCT
ap-6836	21	7	mathematicians	mathematician	NOUN
ap-6836	21	8	are	be	AUX
ap-6836	21	9	interested	interested	ADJ
ap-6836	21	10	in	in	ADP
ap-6836	21	11	palindromic	palindromic	ADJ
ap-6836	21	12	numbers	number	NOUN
ap-6836	21	13	:	:	PUNCT
ap-6836	21	14	positive	positive	ADJ
ap-6836	21	15	integers	integer	NOUN
ap-6836	21	16	whose	whose	DET
ap-6836	21	17	expansion	expansion	NOUN
ap-6836	21	18	in	in	ADP
ap-6836	21	19	a	a	DET
ap-6836	21	20	certain	certain	ADJ
ap-6836	21	21	integer	integer	NOUN
ap-6836	21	22	base	base	NOUN
ap-6836	21	23	is	be	AUX
ap-6836	21	24	a	a	DET
ap-6836	21	25	palindrome	palindrome	NOUN
ap-6836	21	26	.	.	PUNCT
ap-6836	22	1	let	let	VERB
ap-6836	22	2	us	we	PRON
ap-6836	22	3	make	make	VERB
ap-6836	22	4	a	a	DET
ap-6836	22	5	list	list	NOUN
ap-6836	22	6	of	of	ADP
ap-6836	22	7	studied	study	VERB
ap-6836	22	8	problems	problem	NOUN
ap-6836	22	9	:	:	PUNCT
ap-6836	22	10	(	(	PUNCT
ap-6836	22	11	1	1	X
ap-6836	22	12	.	.	PUNCT
ap-6836	22	13	)	)	PUNCT
ap-6836	22	14	palindromic	palindromic	ADJ
ap-6836	22	15	squares	square	NOUN
ap-6836	22	16	,	,	PUNCT
ap-6836	22	17	cubes	cube	NOUN
ap-6836	22	18	,	,	PUNCT
ap-6836	22	19	and	and	CCONJ
ap-6836	22	20	higher	high	ADJ
ap-6836	22	21	powers	power	NOUN
ap-6836	22	22	in	in	ADP
ap-6836	22	23	base	base	NOUN
ap-6836	22	24	10	10	NUM
ap-6836	22	25	:	:	PUNCT
ap-6836	22	26	the	the	DET
ap-6836	22	27	first	first	ADJ
ap-6836	22	28	nine	nine	NUM
ap-6836	22	29	terms	term	NOUN
ap-6836	22	30	of	of	ADP
ap-6836	22	31	the	the	DET
ap-6836	22	32	sequence	sequence	NOUN
ap-6836	22	33	12	12	NUM
ap-6836	22	34	,	,	PUNCT
ap-6836	22	35	112	112	NUM
ap-6836	22	36	,	,	PUNCT
ap-6836	22	37	1112	1112	NUM
ap-6836	22	38	,	,	PUNCT
ap-6836	22	39	11112	11112	NUM
ap-6836	22	40	,	,	PUNCT
ap-6836	22	41	.	.	PUNCT
ap-6836	22	42	.	.	PUNCT
ap-6836	23	1	.	.	PUNCT
ap-6836	24	1	are	be	AUX
ap-6836	24	2	palindromic	palindromic	ADJ
ap-6836	24	3	numbers	number	NOUN
ap-6836	24	4	1	1	NUM
ap-6836	24	5	,	,	PUNCT
ap-6836	24	6	121	121	NUM
ap-6836	24	7	,	,	PUNCT
ap-6836	24	8	12321	12321	NUM
ap-6836	24	9	,	,	PUNCT
ap-6836	24	10	1234321	1234321	NUM
ap-6836	24	11	,	,	PUNCT
ap-6836	24	12	.	.	PUNCT
ap-6836	24	13	.	.	PUNCT
ap-6836	24	14	.	.	PUNCT
ap-6836	25	1	(	(	PUNCT
ap-6836	25	2	sequence	sequence	NOUN
ap-6836	25	3	a002477	a002477	NOUN
ap-6836	25	4	in	in	ADP
ap-6836	25	5	the	the	DET
ap-6836	25	6	oeis	oeis	NOUN
ap-6836	26	1	[	[	X
ap-6836	26	2	2	2	NUM
ap-6836	26	3	]	]	NUM
ap-6836	26	4	)	)	PUNCT
ap-6836	26	5	.	.	PUNCT
ap-6836	27	1	palindromic	palindromic	ADJ
ap-6836	27	2	numbers	number	NOUN
ap-6836	27	3	having	have	VERB
ap-6836	27	4	palindromic	palindromic	ADJ
ap-6836	27	5	squares	square	NOUN
ap-6836	27	6	were	be	AUX
ap-6836	27	7	studied	study	VERB
ap-6836	27	8	in	in	ADP
ap-6836	27	9	[	[	X
ap-6836	27	10	3	3	NUM
ap-6836	27	11	]	]	PUNCT
ap-6836	27	12	.	.	PUNCT
ap-6836	28	1	the	the	DET
ap-6836	28	2	only	only	ADJ
ap-6836	28	3	known	know	VERB
ap-6836	28	4	nonpalindromic	nonpalindromic	ADJ
ap-6836	28	5	number	number	NOUN
ap-6836	28	6	whose	whose	DET
ap-6836	28	7	cube	cube	NOUN
ap-6836	28	8	is	be	AUX
ap-6836	28	9	a	a	DET
ap-6836	28	10	palindromic	palindromic	ADJ
ap-6836	28	11	number	number	NOUN
ap-6836	28	12	is	be	AUX
ap-6836	28	13	2201	2201	NUM
ap-6836	28	14	,	,	PUNCT
ap-6836	28	15	simmons	simmon	VERB
ap-6836	29	1	[	[	X
ap-6836	29	2	4	4	X
ap-6836	29	3	]	]	PUNCT
ap-6836	29	4	conjectured	conjecture	VERB
ap-6836	29	5	that	that	SCONJ
ap-6836	29	6	the	the	DET
ap-6836	29	7	fourth	fourth	ADJ
ap-6836	29	8	root	root	NOUN
ap-6836	29	9	of	of	ADP
ap-6836	29	10	all	all	DET
ap-6836	29	11	palindromic	palindromic	ADJ
ap-6836	29	12	fourth	fourth	ADJ
ap-6836	29	13	powers	power	NOUN
ap-6836	29	14	are	be	AUX
ap-6836	29	15	palindromic	palindromic	ADJ
ap-6836	29	16	numbers	number	NOUN
ap-6836	29	17	of	of	ADP
ap-6836	29	18	the	the	DET
ap-6836	29	19	form	form	NOUN
ap-6836	29	20	10n	10n	NOUN
ap-6836	29	21	+	+	CCONJ
ap-6836	30	1	1	1	X
ap-6836	30	2	.	.	X
ap-6836	30	3	simmons	simmon	NOUN
ap-6836	31	1	[	[	X
ap-6836	31	2	5	5	NUM
ap-6836	31	3	]	]	PUNCT
ap-6836	31	4	also	also	ADV
ap-6836	31	5	conjectured	conjecture	VERB
ap-6836	31	6	there	there	PRON
ap-6836	31	7	are	be	VERB
ap-6836	31	8	no	no	DET
ap-6836	31	9	palindromic	palindromic	ADJ
ap-6836	31	10	numbers	number	NOUN
ap-6836	31	11	of	of	ADP
ap-6836	31	12	the	the	DET
ap-6836	31	13	form	form	NOUN
ap-6836	31	14	nk	nk	PROPN
ap-6836	31	15	for	for	ADP
ap-6836	31	16	k	k	PROPN
ap-6836	31	17	>	>	X
ap-6836	31	18	4	4	NUM
ap-6836	31	19	and	and	CCONJ
ap-6836	31	20	n	n	NOUN
ap-6836	31	21	>	>	X
ap-6836	31	22	1	1	NUM
ap-6836	31	23	.	.	PUNCT
ap-6836	32	1	(	(	PUNCT
ap-6836	32	2	2	2	NUM
ap-6836	32	3	.	.	PUNCT
ap-6836	32	4	)	)	PUNCT
ap-6836	32	5	palindromic	palindromic	ADJ
ap-6836	32	6	primes	prime	NOUN
ap-6836	32	7	:	:	PUNCT
ap-6836	32	8	the	the	DET
ap-6836	32	9	first	first	ADJ
ap-6836	32	10	few	few	ADJ
ap-6836	32	11	decimal	decimal	ADJ
ap-6836	32	12	palindromic	palindromic	ADJ
ap-6836	32	13	primes	prime	NOUN
ap-6836	32	14	are	be	AUX
ap-6836	32	15	(	(	PUNCT
ap-6836	32	16	sequence	sequence	NOUN
ap-6836	32	17	a002385	a002385	PROPN
ap-6836	32	18	in	in	ADP
ap-6836	32	19	the	the	DET
ap-6836	32	20	oeis	oeis	NOUN
ap-6836	33	1	[	[	X
ap-6836	33	2	2	2	NUM
ap-6836	33	3	]	]	SYM
ap-6836	33	4	):	):	PUNCT
ap-6836	33	5	2	2	NUM
ap-6836	33	6	,	,	PUNCT
ap-6836	33	7	3	3	NUM
ap-6836	33	8	,	,	PUNCT
ap-6836	33	9	5	5	NUM
ap-6836	33	10	,	,	PUNCT
ap-6836	33	11	7	7	NUM
ap-6836	33	12	,	,	PUNCT
ap-6836	33	13	11	11	NUM
ap-6836	33	14	,	,	PUNCT
ap-6836	33	15	101	101	NUM
ap-6836	33	16	,	,	PUNCT
ap-6836	33	17	131	131	NUM
ap-6836	33	18	,	,	PUNCT
ap-6836	33	19	151	151	NUM
ap-6836	33	20	,	,	PUNCT
ap-6836	33	21	181	181	NUM
ap-6836	33	22	,	,	PUNCT
ap-6836	33	23	191	191	NUM
ap-6836	33	24	,	,	PUNCT
ap-6836	33	25	313	313	NUM
ap-6836	33	26	,	,	PUNCT
ap-6836	33	27	353	353	NUM
ap-6836	33	28	,	,	PUNCT
ap-6836	33	29	373	373	NUM
ap-6836	33	30	,	,	PUNCT
ap-6836	33	31	383	383	NUM
ap-6836	33	32	,	,	PUNCT
ap-6836	33	33	727	727	NUM
ap-6836	33	34	,	,	PUNCT
ap-6836	33	35	757	757	NUM
ap-6836	33	36	,	,	PUNCT
ap-6836	33	37	787	787	NUM
ap-6836	33	38	,	,	PUNCT
ap-6836	33	39	797	797	NUM
ap-6836	33	40	,	,	PUNCT
ap-6836	33	41	919	919	NUM
ap-6836	33	42	,	,	PUNCT
ap-6836	33	43	929	929	NUM
ap-6836	33	44	,	,	PUNCT
ap-6836	33	45	.	.	PUNCT
ap-6836	33	46	.	.	PUNCT
ap-6836	34	1	.	.	PUNCT
ap-6836	35	1	except	except	SCONJ
ap-6836	35	2	for	for	ADP
ap-6836	35	3	11	11	NUM
ap-6836	35	4	,	,	PUNCT
ap-6836	35	5	all	all	DET
ap-6836	35	6	palindromic	palindromic	ADJ
ap-6836	35	7	primes	prime	NOUN
ap-6836	35	8	have	have	VERB
ap-6836	35	9	an	an	DET
ap-6836	35	10	odd	odd	ADJ
ap-6836	35	11	number	number	NOUN
ap-6836	35	12	of	of	ADP
ap-6836	35	13	digits	digit	NOUN
ap-6836	35	14	because	because	SCONJ
ap-6836	35	15	the	the	DET
ap-6836	35	16	divisibility	divisibility	NOUN
ap-6836	35	17	test	test	NOUN
ap-6836	35	18	for	for	ADP
ap-6836	35	19	11	11	NUM
ap-6836	35	20	tells	tell	VERB
ap-6836	35	21	us	we	PRON
ap-6836	35	22	that	that	SCONJ
ap-6836	35	23	every	every	DET
ap-6836	35	24	palindromic	palindromic	ADJ
ap-6836	35	25	number	number	NOUN
ap-6836	35	26	with	with	ADP
ap-6836	35	27	an	an	DET
ap-6836	35	28	even	even	ADJ
ap-6836	35	29	number	number	NOUN
ap-6836	35	30	of	of	ADP
ap-6836	35	31	digits	digit	NOUN
ap-6836	35	32	is	be	AUX
ap-6836	35	33	divisible	divisible	ADJ
ap-6836	35	34	by	by	ADP
ap-6836	35	35	11	11	NUM
ap-6836	35	36	.	.	PUNCT
ap-6836	36	1	on	on	ADP
ap-6836	36	2	the	the	DET
ap-6836	36	3	one	one	NUM
ap-6836	36	4	hand	hand	NOUN
ap-6836	36	5	,	,	PUNCT
ap-6836	36	6	it	it	PRON
ap-6836	36	7	is	be	AUX
ap-6836	36	8	not	not	PART
ap-6836	36	9	known	know	VERB
ap-6836	36	10	if	if	SCONJ
ap-6836	36	11	there	there	PRON
ap-6836	36	12	are	be	VERB
ap-6836	36	13	infinitely	infinitely	ADV
ap-6836	36	14	many	many	ADJ
ap-6836	36	15	palindromic	palindromic	ADJ
ap-6836	36	16	primes	prime	NOUN
ap-6836	36	17	in	in	ADP
ap-6836	36	18	base	base	NOUN
ap-6836	36	19	10	10	NUM
ap-6836	36	20	;	;	PUNCT
ap-6836	36	21	the	the	DET
ap-6836	36	22	largest	large	ADJ
ap-6836	36	23	known	know	VERB
ap-6836	36	24	decimal	decimal	ADJ
ap-6836	36	25	palindromic	palindromic	ADJ
ap-6836	36	26	prime	prime	NOUN
ap-6836	36	27	has	have	VERB
ap-6836	36	28	474,501	474,501	NUM
ap-6836	36	29	digits	digit	NOUN
ap-6836	36	30	(	(	PUNCT
ap-6836	36	31	found	find	VERB
ap-6836	36	32	in	in	ADP
ap-6836	36	33	2014	2014	NUM
ap-6836	36	34	):	):	PUNCT
ap-6836	36	35	10474500	10474500	NUM
ap-6836	36	36	+	+	CCONJ
ap-6836	36	37	999	999	NUM
ap-6836	36	38	·	·	SYM
ap-6836	36	39	10237249	10237249	NUM
ap-6836	37	1	+	+	CCONJ
ap-6836	37	2	1	1	X
ap-6836	37	3	.	.	X
ap-6836	37	4	on	on	ADP
ap-6836	37	5	the	the	DET
ap-6836	37	6	other	other	ADJ
ap-6836	37	7	hand	hand	NOUN
ap-6836	37	8	,	,	PUNCT
ap-6836	37	9	it	it	PRON
ap-6836	37	10	is	be	AUX
ap-6836	37	11	known	know	VERB
ap-6836	37	12	that	that	SCONJ
ap-6836	37	13	,	,	PUNCT
ap-6836	37	14	for	for	ADP
ap-6836	37	15	any	any	DET
ap-6836	37	16	base	base	NOUN
ap-6836	37	17	,	,	PUNCT
ap-6836	37	18	almost	almost	ADV
ap-6836	37	19	all	all	PRON
ap-6836	37	20	palindromic	palindromic	ADJ
ap-6836	37	21	numbers	number	NOUN
ap-6836	37	22	are	be	AUX
ap-6836	37	23	composite	composite	ADJ
ap-6836	37	24	[	[	X
ap-6836	37	25	6	6	NUM
ap-6836	37	26	]	]	PUNCT
ap-6836	37	27	.	.	PUNCT
ap-6836	38	1	it	it	PRON
ap-6836	38	2	means	mean	VERB
ap-6836	38	3	that	that	SCONJ
ap-6836	38	4	the	the	DET
ap-6836	38	5	ratio	ratio	NOUN
ap-6836	38	6	of	of	ADP
ap-6836	38	7	palindromic	palindromic	ADJ
ap-6836	38	8	composites	composite	NOUN
ap-6836	38	9	and	and	CCONJ
ap-6836	38	10	all	all	DET
ap-6836	38	11	palindromic	palindromic	ADJ
ap-6836	38	12	numbers	number	NOUN
ap-6836	38	13	less	less	ADJ
ap-6836	38	14	than	than	ADP
ap-6836	38	15	n	n	PRON
ap-6836	38	16	tends	tend	VERB
ap-6836	38	17	to	to	ADP
ap-6836	38	18	1	1	NUM
ap-6836	38	19	.	.	PUNCT
ap-6836	38	20	binary	binary	ADJ
ap-6836	38	21	palindromic	palindromic	ADJ
ap-6836	38	22	primes	prime	NOUN
ap-6836	38	23	include	include	VERB
ap-6836	38	24	the	the	DET
ap-6836	38	25	mersenne	mersenne	NOUN
ap-6836	38	26	primes	prime	NOUN
ap-6836	38	27	and	and	CCONJ
ap-6836	38	28	the	the	DET
ap-6836	38	29	fermat	fermat	PROPN
ap-6836	38	30	primes	prime	VERB
ap-6836	38	31	1	1	NUM
ap-6836	38	32	.	.	PUNCT
ap-6836	39	1	all	all	DET
ap-6836	39	2	binary	binary	ADJ
ap-6836	39	3	palindromic	palindromic	ADJ
ap-6836	39	4	primes	prime	NOUN
ap-6836	39	5	,	,	PUNCT
ap-6836	39	6	except	except	SCONJ
ap-6836	39	7	the	the	DET
ap-6836	39	8	number	number	NOUN
ap-6836	39	9	3	3	NUM
ap-6836	39	10	(	(	PUNCT
ap-6836	39	11	having	have	VERB
ap-6836	39	12	the	the	DET
ap-6836	39	13	expansion	expansion	NOUN
ap-6836	39	14	11	11	NUM
ap-6836	39	15	in	in	ADP
ap-6836	39	16	base	base	NOUN
ap-6836	39	17	2	2	NUM
ap-6836	39	18	)	)	PUNCT
ap-6836	39	19	,	,	PUNCT
ap-6836	39	20	have	have	VERB
ap-6836	39	21	an	an	DET
ap-6836	39	22	odd	odd	ADJ
ap-6836	39	23	number	number	NOUN
ap-6836	39	24	of	of	ADP
ap-6836	39	25	digits	digit	NOUN
ap-6836	39	26	;	;	PUNCT
ap-6836	39	27	palindromic	palindromic	ADJ
ap-6836	39	28	numbers	number	NOUN
ap-6836	39	29	with	with	ADP
ap-6836	39	30	an	an	DET
ap-6836	39	31	even	even	ADJ
ap-6836	39	32	number	number	NOUN
ap-6836	39	33	of	of	ADP
ap-6836	39	34	digits	digit	NOUN
ap-6836	39	35	are	be	AUX
ap-6836	39	36	divisible	divisible	ADJ
ap-6836	39	37	by	by	ADP
ap-6836	39	38	3	3	NUM
ap-6836	39	39	.	.	PUNCT
ap-6836	40	1	let	let	VERB
ap-6836	40	2	us	we	PRON
ap-6836	40	3	write	write	VERB
ap-6836	40	4	down	down	ADP
ap-6836	40	5	1a	1a	PROPN
ap-6836	40	6	mersenne	mersenne	PROPN
ap-6836	40	7	prime	prime	PROPN
ap-6836	40	8	is	be	AUX
ap-6836	40	9	a	a	DET
ap-6836	40	10	prime	prime	NOUN
ap-6836	40	11	of	of	ADP
ap-6836	40	12	the	the	DET
ap-6836	40	13	form	form	NOUN
ap-6836	40	14	2p	2p	NUM
ap-6836	40	15	−	−	NOUN
ap-6836	40	16	1	1	NUM
ap-6836	40	17	,	,	PUNCT
ap-6836	40	18	where	where	SCONJ
ap-6836	40	19	p	p	NOUN
ap-6836	40	20	is	be	AUX
ap-6836	40	21	a	a	DET
ap-6836	40	22	prime	prime	NOUN
ap-6836	40	23	.	.	PUNCT
ap-6836	41	1	a	a	DET
ap-6836	41	2	fermat	fermat	PROPN
ap-6836	41	3	prime	prime	NOUN
ap-6836	41	4	is	be	AUX
ap-6836	41	5	a	a	DET
ap-6836	41	6	prime	prime	NOUN
ap-6836	41	7	of	of	ADP
ap-6836	41	8	the	the	DET
ap-6836	41	9	form	form	NOUN
ap-6836	41	10	22n	22n	NOUN
ap-6836	41	11	+	+	CCONJ
ap-6836	41	12	1	1	NUM
ap-6836	41	13	.	.	X
ap-6836	41	14	428	428	NUM
ap-6836	41	15	https://doi.org/10.14311/ap.2021.61.0428	https://doi.org/10.14311/ap.2021.61.0428	ADP
ap-6836	41	16	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
ap-6836	41	17	https://www.cvut.cz/en	https://www.cvut.cz/en	PROPN
ap-6836	41	18	vol	vol	NOUN
ap-6836	41	19	.	.	PROPN
ap-6836	42	1	61	61	NUM
ap-6836	42	2	no	no	NOUN
ap-6836	42	3	.	.	PUNCT
ap-6836	43	1	3/2021	3/2021	NUM
ap-6836	43	2	antipalindromic	antipalindromic	ADJ
ap-6836	43	3	numbers	number	NOUN
ap-6836	43	4	the	the	DET
ap-6836	43	5	sequence	sequence	NOUN
ap-6836	43	6	of	of	ADP
ap-6836	43	7	binary	binary	ADJ
ap-6836	43	8	expansions	expansion	NOUN
ap-6836	43	9	of	of	ADP
ap-6836	43	10	the	the	DET
ap-6836	43	11	first	first	ADJ
ap-6836	43	12	binary	binary	ADJ
ap-6836	43	13	palindromic	palindromic	ADJ
ap-6836	43	14	primes	prime	NOUN
ap-6836	43	15	(	(	PUNCT
ap-6836	43	16	sequence	sequence	NOUN
ap-6836	43	17	a117697	a117697	VERB
ap-6836	43	18	in	in	ADP
ap-6836	43	19	the	the	DET
ap-6836	43	20	oeis	oeis	NOUN
ap-6836	44	1	[	[	X
ap-6836	44	2	2	2	NUM
ap-6836	44	3	]	]	SYM
ap-6836	44	4	):	):	PUNCT
ap-6836	44	5	11	11	NUM
ap-6836	44	6	,	,	PUNCT
ap-6836	44	7	101	101	NUM
ap-6836	44	8	,	,	PUNCT
ap-6836	44	9	111	111	NUM
ap-6836	44	10	,	,	PUNCT
ap-6836	44	11	10001	10001	NUM
ap-6836	44	12	,	,	PUNCT
ap-6836	44	13	11111	11111	NUM
ap-6836	44	14	,	,	PUNCT
ap-6836	44	15	1001001	1001001	NUM
ap-6836	44	16	,	,	PUNCT
ap-6836	44	17	1101011	1101011	NUM
ap-6836	44	18	,	,	PUNCT
ap-6836	44	19	1111111	1111111	NUM
ap-6836	44	20	,	,	PUNCT
ap-6836	44	21	100000001	100000001	NUM
ap-6836	44	22	,	,	PUNCT
ap-6836	44	23	100111001	100111001	NUM
ap-6836	44	24	,	,	PUNCT
ap-6836	44	25	110111011	110111011	NUM
ap-6836	44	26	,	,	PUNCT
ap-6836	44	27	.	.	PUNCT
ap-6836	44	28	.	.	PUNCT
ap-6836	44	29	.	.	PUNCT
ap-6836	45	1	(	(	PUNCT
ap-6836	45	2	3	3	X
ap-6836	45	3	.	.	PUNCT
ap-6836	45	4	)	)	PUNCT
ap-6836	45	5	multi	multi	ADJ
ap-6836	45	6	-	-	ADJ
ap-6836	45	7	base	base	ADJ
ap-6836	45	8	palindromic	palindromic	ADJ
ap-6836	45	9	numbers	number	NOUN
ap-6836	45	10	:	:	PUNCT
ap-6836	45	11	any	any	DET
ap-6836	45	12	positive	positive	ADJ
ap-6836	45	13	integer	integer	NOUN
ap-6836	45	14	n	n	PRON
ap-6836	45	15	is	be	AUX
ap-6836	45	16	palindromic	palindromic	ADJ
ap-6836	45	17	in	in	ADP
ap-6836	45	18	all	all	DET
ap-6836	45	19	bases	basis	NOUN
ap-6836	45	20	b	b	NOUN
ap-6836	45	21	with	with	ADP
ap-6836	45	22	b	b	PROPN
ap-6836	45	23	≥	≥	NOUN
ap-6836	45	24	n+1	n+1	NUM
ap-6836	45	25	because	because	SCONJ
ap-6836	45	26	n	n	X
ap-6836	45	27	is	be	AUX
ap-6836	45	28	then	then	ADV
ap-6836	45	29	a	a	DET
ap-6836	45	30	single	single	ADJ
ap-6836	45	31	-	-	PUNCT
ap-6836	45	32	digit	digit	NOUN
ap-6836	45	33	number	number	NOUN
ap-6836	45	34	,	,	PUNCT
ap-6836	45	35	and	and	CCONJ
ap-6836	45	36	also	also	ADV
ap-6836	45	37	in	in	ADP
ap-6836	45	38	base	base	NOUN
ap-6836	45	39	n	n	CCONJ
ap-6836	45	40	−	−	PROPN
ap-6836	45	41	1	1	NUM
ap-6836	45	42	because	because	SCONJ
ap-6836	45	43	the	the	DET
ap-6836	45	44	expansion	expansion	NOUN
ap-6836	45	45	of	of	ADP
ap-6836	45	46	n	n	PROPN
ap-6836	45	47	in	in	ADP
ap-6836	45	48	base	base	NOUN
ap-6836	45	49	n	n	CCONJ
ap-6836	45	50	−	−	PROPN
ap-6836	45	51	1	1	NUM
ap-6836	45	52	equals	equal	VERB
ap-6836	45	53	11	11	NUM
ap-6836	45	54	.	.	PUNCT
ap-6836	46	1	but	but	CCONJ
ap-6836	46	2	,	,	PUNCT
ap-6836	46	3	it	it	PRON
ap-6836	46	4	is	be	AUX
ap-6836	46	5	more	more	ADV
ap-6836	46	6	interesting	interesting	ADJ
ap-6836	46	7	to	to	PART
ap-6836	46	8	consider	consider	VERB
ap-6836	46	9	bases	basis	NOUN
ap-6836	46	10	smaller	small	ADJ
ap-6836	46	11	than	than	ADP
ap-6836	46	12	the	the	DET
ap-6836	46	13	number	number	NOUN
ap-6836	46	14	itself	itself	PRON
ap-6836	46	15	.	.	PUNCT
ap-6836	47	1	for	for	ADP
ap-6836	47	2	instance	instance	NOUN
ap-6836	47	3	,	,	PUNCT
ap-6836	47	4	the	the	DET
ap-6836	47	5	number	number	NOUN
ap-6836	47	6	105	105	NUM
ap-6836	47	7	is	be	AUX
ap-6836	47	8	palindromic	palindromic	ADJ
ap-6836	47	9	in	in	ADP
ap-6836	47	10	bases	basis	NOUN
ap-6836	47	11	4	4	NUM
ap-6836	47	12	,	,	PUNCT
ap-6836	47	13	8	8	NUM
ap-6836	47	14	,	,	PUNCT
ap-6836	47	15	14	14	NUM
ap-6836	47	16	,	,	PUNCT
ap-6836	47	17	20	20	NUM
ap-6836	47	18	,	,	PUNCT
ap-6836	47	19	34	34	NUM
ap-6836	47	20	,	,	PUNCT
ap-6836	47	21	104	104	NUM
ap-6836	47	22	;	;	PUNCT
ap-6836	47	23	the	the	DET
ap-6836	47	24	expansions	expansion	NOUN
ap-6836	47	25	of	of	ADP
ap-6836	47	26	105	105	NUM
ap-6836	47	27	in	in	ADP
ap-6836	47	28	those	those	DET
ap-6836	47	29	bases	basis	NOUN
ap-6836	47	30	are	be	AUX
ap-6836	47	31	:	:	PUNCT
ap-6836	47	32	(	(	PUNCT
ap-6836	47	33	105)4	105)4	NUM
ap-6836	47	34	=	=	SYM
ap-6836	47	35	1221	1221	NUM
ap-6836	47	36	,	,	PUNCT
ap-6836	47	37	(	(	PUNCT
ap-6836	47	38	105)8	105)8	NUM
ap-6836	47	39	=	=	SYM
ap-6836	47	40	151	151	NUM
ap-6836	47	41	,	,	PUNCT
ap-6836	47	42	(	(	PUNCT
ap-6836	47	43	105)14	105)14	PROPN
ap-6836	47	44	=	=	SYM
ap-6836	47	45	77	77	NUM
ap-6836	47	46	,	,	PUNCT
ap-6836	47	47	(	(	PUNCT
ap-6836	47	48	105)20	105)20	NUM
ap-6836	47	49	=	=	SYM
ap-6836	47	50	55	55	NUM
ap-6836	47	51	,	,	PUNCT
ap-6836	47	52	(	(	PUNCT
ap-6836	47	53	105)34	105)34	NUM
ap-6836	47	54	=	=	SYM
ap-6836	47	55	33	33	NUM
ap-6836	47	56	,	,	PUNCT
ap-6836	47	57	(	(	PUNCT
ap-6836	47	58	105)104	105)104	NOUN
ap-6836	48	1	=	=	SYM
ap-6836	49	1	11	11	NUM
ap-6836	49	2	.	.	PUNCT
ap-6836	50	1	a	a	DET
ap-6836	50	2	palindromic	palindromic	ADJ
ap-6836	50	3	number	number	NOUN
ap-6836	50	4	in	in	ADP
ap-6836	50	5	base	base	PROPN
ap-6836	50	6	b	b	PROPN
ap-6836	50	7	whose	whose	DET
ap-6836	50	8	expansion	expansion	NOUN
ap-6836	50	9	is	be	AUX
ap-6836	50	10	made	make	VERB
ap-6836	50	11	up	up	ADP
ap-6836	50	12	of	of	ADP
ap-6836	50	13	palindromic	palindromic	ADJ
ap-6836	50	14	sequences	sequence	NOUN
ap-6836	50	15	of	of	ADP
ap-6836	50	16	length	length	NOUN
ap-6836	50	17	`	`	PUNCT
ap-6836	50	18	arranged	arrange	VERB
ap-6836	50	19	in	in	ADP
ap-6836	50	20	a	a	DET
ap-6836	50	21	palindromic	palindromic	ADJ
ap-6836	50	22	order	order	NOUN
ap-6836	50	23	is	be	AUX
ap-6836	50	24	palindromic	palindromic	ADJ
ap-6836	50	25	in	in	ADP
ap-6836	50	26	base	base	NOUN
ap-6836	50	27	b	b	NOUN
ap-6836	50	28	`	`	PUNCT
ap-6836	50	29	.	.	PUNCT
ap-6836	51	1	for	for	ADP
ap-6836	51	2	example	example	NOUN
ap-6836	51	3	,	,	PUNCT
ap-6836	51	4	the	the	DET
ap-6836	51	5	number	number	NOUN
ap-6836	51	6	24253	24253	NUM
ap-6836	51	7	has	have	VERB
ap-6836	51	8	the	the	DET
ap-6836	51	9	expansion	expansion	NOUN
ap-6836	51	10	in	in	ADP
ap-6836	51	11	base	base	NOUN
ap-6836	51	12	2	2	NUM
ap-6836	51	13	equal	equal	ADJ
ap-6836	51	14	to	to	ADP
ap-6836	51	15	(	(	PUNCT
ap-6836	51	16	24253)2	24253)2	NUM
ap-6836	51	17	=	=	SYM
ap-6836	51	18	101	101	NUM
ap-6836	51	19	111	111	NUM
ap-6836	51	20	010	010	NUM
ap-6836	51	21	111	111	NUM
ap-6836	51	22	101	101	NUM
ap-6836	51	23	,	,	PUNCT
ap-6836	51	24	i.e.	i.e.	X
ap-6836	51	25	,	,	PUNCT
ap-6836	51	26	it	it	PRON
ap-6836	51	27	is	be	AUX
ap-6836	51	28	made	make	VERB
ap-6836	51	29	up	up	ADP
ap-6836	51	30	of	of	ADP
ap-6836	51	31	palindromes	palindrome	NOUN
ap-6836	51	32	of	of	ADP
ap-6836	51	33	length	length	NOUN
ap-6836	51	34	of	of	ADP
ap-6836	51	35	3	3	NUM
ap-6836	51	36	,	,	PUNCT
ap-6836	51	37	and	and	CCONJ
ap-6836	51	38	its	its	PRON
ap-6836	51	39	expansion	expansion	NOUN
ap-6836	51	40	in	in	ADP
ap-6836	51	41	base	base	NOUN
ap-6836	51	42	23	23	NUM
ap-6836	51	43	=	=	SYM
ap-6836	51	44	8	8	NUM
ap-6836	51	45	is	be	AUX
ap-6836	51	46	equal	equal	ADJ
ap-6836	51	47	to	to	ADP
ap-6836	51	48	(	(	PUNCT
ap-6836	51	49	24253)8	24253)8	NUM
ap-6836	51	50	=	=	SYM
ap-6836	51	51	57275	57275	NUM
ap-6836	51	52	.	.	PUNCT
ap-6836	52	1	(	(	PUNCT
ap-6836	52	2	4	4	NUM
ap-6836	52	3	.	.	PUNCT
ap-6836	52	4	)	)	PUNCT
ap-6836	52	5	sum	sum	NOUN
ap-6836	52	6	of	of	ADP
ap-6836	52	7	palindromes	palindrome	NOUN
ap-6836	52	8	:	:	PUNCT
ap-6836	52	9	every	every	DET
ap-6836	52	10	positive	positive	ADJ
ap-6836	52	11	integer	integer	NOUN
ap-6836	52	12	can	can	AUX
ap-6836	52	13	be	be	AUX
ap-6836	52	14	written	write	VERB
ap-6836	52	15	as	as	ADP
ap-6836	52	16	the	the	DET
ap-6836	52	17	sum	sum	NOUN
ap-6836	52	18	of	of	ADP
ap-6836	52	19	at	at	ADV
ap-6836	52	20	most	most	ADV
ap-6836	52	21	three	three	NUM
ap-6836	52	22	palindromic	palindromic	ADJ
ap-6836	52	23	numbers	number	NOUN
ap-6836	52	24	in	in	ADP
ap-6836	52	25	every	every	DET
ap-6836	52	26	number	number	NOUN
ap-6836	52	27	system	system	NOUN
ap-6836	52	28	except	except	SCONJ
ap-6836	52	29	the	the	DET
ap-6836	52	30	binary	binary	ADJ
ap-6836	52	31	system	system	NOUN
ap-6836	52	32	.	.	PUNCT
ap-6836	53	1	it	it	PRON
ap-6836	53	2	was	be	AUX
ap-6836	53	3	proven	prove	VERB
ap-6836	53	4	first	first	ADV
ap-6836	53	5	for	for	ADP
ap-6836	53	6	bases	basis	NOUN
ap-6836	53	7	greater	great	ADJ
ap-6836	53	8	than	than	ADP
ap-6836	53	9	or	or	CCONJ
ap-6836	53	10	equal	equal	ADJ
ap-6836	53	11	to	to	ADP
ap-6836	53	12	5	5	NUM
ap-6836	53	13	in	in	ADP
ap-6836	53	14	[	[	X
ap-6836	53	15	7	7	NUM
ap-6836	53	16	]	]	PUNCT
ap-6836	53	17	and	and	CCONJ
ap-6836	53	18	for	for	ADP
ap-6836	53	19	bases	basis	NOUN
ap-6836	53	20	3	3	NUM
ap-6836	53	21	,	,	PUNCT
ap-6836	53	22	4	4	NUM
ap-6836	53	23	in	in	ADP
ap-6836	53	24	[	[	X
ap-6836	53	25	8	8	NUM
ap-6836	53	26	]	]	PUNCT
ap-6836	53	27	.	.	PUNCT
ap-6836	54	1	moreover	moreover	ADV
ap-6836	54	2	,	,	PUNCT
ap-6836	54	3	the	the	DET
ap-6836	54	4	optimal	optimal	ADJ
ap-6836	54	5	bound	bind	VERB
ap-6836	54	6	for	for	ADP
ap-6836	54	7	base	base	NOUN
ap-6836	54	8	2	2	NUM
ap-6836	54	9	is	be	AUX
ap-6836	54	10	four	four	NUM
ap-6836	54	11	,	,	PUNCT
ap-6836	54	12	see	see	VERB
ap-6836	54	13	[	[	X
ap-6836	54	14	8	8	NUM
ap-6836	54	15	]	]	PUNCT
ap-6836	54	16	.	.	PUNCT
ap-6836	55	1	in	in	ADP
ap-6836	55	2	this	this	DET
ap-6836	55	3	paper	paper	NOUN
ap-6836	55	4	,	,	PUNCT
ap-6836	55	5	we	we	PRON
ap-6836	55	6	deal	deal	VERB
ap-6836	55	7	with	with	ADP
ap-6836	55	8	antipalindromic	antipalindromic	ADJ
ap-6836	55	9	numbers	number	NOUN
ap-6836	55	10	in	in	ADP
ap-6836	55	11	various	various	ADJ
ap-6836	55	12	integer	integer	NOUN
ap-6836	55	13	bases	basis	NOUN
ap-6836	55	14	.	.	PUNCT
ap-6836	56	1	we	we	PRON
ap-6836	56	2	examine	examine	VERB
ap-6836	56	3	and	and	CCONJ
ap-6836	56	4	compare	compare	VERB
ap-6836	56	5	properties	property	NOUN
ap-6836	56	6	of	of	ADP
ap-6836	56	7	palindromic	palindromic	ADJ
ap-6836	56	8	numbers	number	NOUN
ap-6836	56	9	and	and	CCONJ
ap-6836	56	10	antipalindromic	antipalindromic	ADJ
ap-6836	56	11	numbers	number	NOUN
ap-6836	56	12	,	,	PUNCT
ap-6836	56	13	bringing	bring	VERB
ap-6836	56	14	a	a	DET
ap-6836	56	15	number	number	NOUN
ap-6836	56	16	of	of	ADP
ap-6836	56	17	new	new	ADJ
ap-6836	56	18	results	result	NOUN
ap-6836	56	19	.	.	PUNCT
ap-6836	57	1	these	these	PRON
ap-6836	57	2	are	be	AUX
ap-6836	57	3	structured	structure	VERB
ap-6836	57	4	as	as	SCONJ
ap-6836	57	5	follows	follow	VERB
ap-6836	57	6	.	.	PUNCT
ap-6836	58	1	in	in	ADP
ap-6836	58	2	section	section	NOUN
ap-6836	58	3	2	2	NUM
ap-6836	58	4	,	,	PUNCT
ap-6836	58	5	we	we	PRON
ap-6836	58	6	introduce	introduce	VERB
ap-6836	58	7	the	the	DET
ap-6836	58	8	definition	definition	NOUN
ap-6836	58	9	of	of	ADP
ap-6836	58	10	an	an	DET
ap-6836	58	11	antipalindromic	antipalindromic	ADJ
ap-6836	58	12	number	number	NOUN
ap-6836	58	13	in	in	ADP
ap-6836	58	14	an	an	DET
ap-6836	58	15	integer	integer	NOUN
ap-6836	58	16	base	base	NOUN
ap-6836	58	17	and	and	CCONJ
ap-6836	58	18	its	its	PRON
ap-6836	58	19	basic	basic	ADJ
ap-6836	58	20	properties	property	NOUN
ap-6836	58	21	,	,	PUNCT
ap-6836	58	22	following	follow	VERB
ap-6836	58	23	from	from	ADP
ap-6836	58	24	the	the	DET
ap-6836	58	25	definition	definition	NOUN
ap-6836	58	26	.	.	PUNCT
ap-6836	59	1	section	section	NOUN
ap-6836	59	2	3	3	NUM
ap-6836	59	3	brings	bring	VERB
ap-6836	59	4	unexpected	unexpected	ADJ
ap-6836	59	5	results	result	NOUN
ap-6836	59	6	concerning	concern	VERB
ap-6836	59	7	divisibility	divisibility	NOUN
ap-6836	59	8	and	and	CCONJ
ap-6836	59	9	antipalindromic	antipalindromic	ADJ
ap-6836	59	10	primes	prime	NOUN
ap-6836	59	11	.	.	PUNCT
ap-6836	60	1	in	in	ADP
ap-6836	60	2	section	section	NOUN
ap-6836	60	3	4	4	NUM
ap-6836	60	4	,	,	PUNCT
ap-6836	60	5	antipalindromic	antipalindromic	ADJ
ap-6836	60	6	squares	square	NOUN
ap-6836	60	7	and	and	CCONJ
ap-6836	60	8	higher	high	ADJ
ap-6836	60	9	powers	power	NOUN
ap-6836	60	10	are	be	AUX
ap-6836	60	11	examined	examine	VERB
ap-6836	60	12	.	.	PUNCT
ap-6836	61	1	section	section	NOUN
ap-6836	61	2	5	5	NUM
ap-6836	61	3	contains	contain	VERB
ap-6836	61	4	information	information	NOUN
ap-6836	61	5	about	about	ADP
ap-6836	61	6	numbers	number	NOUN
ap-6836	61	7	that	that	PRON
ap-6836	61	8	are	be	AUX
ap-6836	61	9	antipalindromic	antipalindromic	ADJ
ap-6836	61	10	in	in	ADP
ap-6836	61	11	two	two	NUM
ap-6836	61	12	or	or	CCONJ
ap-6836	61	13	more	more	ADJ
ap-6836	61	14	bases	basis	NOUN
ap-6836	61	15	at	at	ADP
ap-6836	61	16	the	the	DET
ap-6836	61	17	same	same	ADJ
ap-6836	61	18	time	time	NOUN
ap-6836	61	19	.	.	PUNCT
ap-6836	62	1	in	in	ADP
ap-6836	62	2	section	section	NOUN
ap-6836	62	3	6	6	NUM
ap-6836	62	4	,	,	PUNCT
ap-6836	62	5	we	we	PRON
ap-6836	62	6	summarize	summarize	VERB
ap-6836	62	7	our	our	PRON
ap-6836	62	8	results	result	NOUN
ap-6836	62	9	and	and	CCONJ
ap-6836	62	10	provide	provide	VERB
ap-6836	62	11	a	a	DET
ap-6836	62	12	list	list	NOUN
ap-6836	62	13	of	of	ADP
ap-6836	62	14	conjectures	conjecture	NOUN
ap-6836	62	15	and	and	CCONJ
ap-6836	62	16	open	open	ADJ
ap-6836	62	17	problems	problem	NOUN
ap-6836	62	18	.	.	PUNCT
ap-6836	63	1	2	2	X
ap-6836	63	2	.	.	X
ap-6836	63	3	definition	definition	NOUN
ap-6836	63	4	and	and	CCONJ
ap-6836	63	5	basic	basic	ADJ
ap-6836	63	6	properties	property	NOUN
ap-6836	63	7	let	let	VERB
ap-6836	63	8	us	we	PRON
ap-6836	63	9	start	start	VERB
ap-6836	63	10	with	with	ADP
ap-6836	63	11	a	a	DET
ap-6836	63	12	formal	formal	ADJ
ap-6836	63	13	definition	definition	NOUN
ap-6836	63	14	of	of	ADP
ap-6836	63	15	palindromic	palindromic	ADJ
ap-6836	63	16	and	and	CCONJ
ap-6836	63	17	antipalindromic	antipalindromic	ADJ
ap-6836	63	18	numbers	number	NOUN
ap-6836	63	19	and	and	CCONJ
ap-6836	63	20	their	their	PRON
ap-6836	63	21	basic	basic	ADJ
ap-6836	63	22	properties	property	NOUN
ap-6836	63	23	.	.	PUNCT
ap-6836	64	1	definition	definition	NOUN
ap-6836	64	2	1	1	NUM
ap-6836	64	3	.	.	PUNCT
ap-6836	65	1	let	let	VERB
ap-6836	65	2	b	b	PROPN
ap-6836	65	3	∈	∈	PROPN
ap-6836	65	4	n	n	CCONJ
ap-6836	65	5	,	,	PUNCT
ap-6836	65	6	b	b	PROPN
ap-6836	65	7	≥	≥	NUM
ap-6836	65	8	2	2	NUM
ap-6836	65	9	.	.	PUNCT
ap-6836	65	10	consider	consider	VERB
ap-6836	65	11	a	a	DET
ap-6836	65	12	natural	natural	ADJ
ap-6836	65	13	number	number	NOUN
ap-6836	65	14	m	m	VERB
ap-6836	65	15	whose	whose	DET
ap-6836	65	16	expansion	expansion	NOUN
ap-6836	65	17	in	in	ADP
ap-6836	65	18	base	base	PROPN
ap-6836	65	19	b	b	PROPN
ap-6836	65	20	is	be	AUX
ap-6836	65	21	of	of	ADP
ap-6836	65	22	the	the	DET
ap-6836	65	23	following	follow	VERB
ap-6836	65	24	form	form	NOUN
ap-6836	65	25	m	m	VERB
ap-6836	65	26	=	=	PUNCT
ap-6836	65	27	anbn	anbn	PROPN
ap-6836	65	28	+	+	NUM
ap-6836	65	29	·	·	PUNCT
ap-6836	65	30	·	·	PUNCT
ap-6836	65	31	·	·	PUNCT
ap-6836	65	32	+	+	NUM
ap-6836	65	33	a1b	a1b	PROPN
ap-6836	65	34	+	+	CCONJ
ap-6836	65	35	a0	a0	PROPN
ap-6836	65	36	,	,	PUNCT
ap-6836	65	37	where	where	SCONJ
ap-6836	65	38	a0	a0	PROPN
ap-6836	65	39	,	,	PUNCT
ap-6836	65	40	a1	a1	PROPN
ap-6836	65	41	,	,	PUNCT
ap-6836	65	42	.	.	PUNCT
ap-6836	65	43	.	.	PUNCT
ap-6836	66	1	.	.	PUNCT
ap-6836	67	1	,	,	PUNCT
ap-6836	67	2	an	an	DET
ap-6836	67	3	∈	∈	NOUN
ap-6836	67	4	{	{	PUNCT
ap-6836	67	5	0	0	NUM
ap-6836	67	6	,	,	PUNCT
ap-6836	67	7	1	1	NUM
ap-6836	67	8	,	,	PUNCT
ap-6836	67	9	.	.	PUNCT
ap-6836	67	10	.	.	PUNCT
ap-6836	67	11	.	.	PUNCT
ap-6836	68	1	,	,	PUNCT
ap-6836	69	1	b	b	X
ap-6836	69	2	−	−	NOUN
ap-6836	69	3	1	1	NUM
ap-6836	69	4	}	}	PUNCT
ap-6836	69	5	,	,	PUNCT
ap-6836	69	6	an	an	DET
ap-6836	69	7	6=	6=	NUM
ap-6836	69	8	0	0	NUM
ap-6836	69	9	.	.	PUNCT
ap-6836	70	1	we	we	PRON
ap-6836	70	2	usually	usually	ADV
ap-6836	70	3	write	write	VERB
ap-6836	70	4	(	(	PUNCT
ap-6836	70	5	m)b	m)b	NOUN
ap-6836	70	6	=	=	PUNCT
ap-6836	70	7	an	an	PRON
ap-6836	70	8	.	.	PUNCT
ap-6836	70	9	.	.	PUNCT
ap-6836	70	10	.	.	PUNCT
ap-6836	71	1	a1a0	a1a0	X
ap-6836	71	2	.	.	PUNCT
ap-6836	72	1	then	then	ADV
ap-6836	72	2	m	m	PROPN
ap-6836	72	3	is	be	AUX
ap-6836	72	4	called	call	VERB
ap-6836	72	5	(	(	PUNCT
ap-6836	72	6	1	1	NUM
ap-6836	72	7	.	.	PUNCT
ap-6836	72	8	)	)	PUNCT
ap-6836	73	1	a	a	DET
ap-6836	73	2	palindromic	palindromic	ADJ
ap-6836	73	3	number	number	NOUN
ap-6836	73	4	in	in	ADP
ap-6836	73	5	base	base	PROPN
ap-6836	73	6	b	b	PROPN
ap-6836	73	7	if	if	SCONJ
ap-6836	73	8	its	its	PRON
ap-6836	73	9	digits	digit	NOUN
ap-6836	73	10	satisfy	satisfy	VERB
ap-6836	73	11	the	the	DET
ap-6836	73	12	condition	condition	NOUN
ap-6836	73	13	:	:	PUNCT
ap-6836	73	14	aj	aj	PROPN
ap-6836	73	15	=	=	PROPN
ap-6836	73	16	an−j	an−j	ADV
ap-6836	73	17	for	for	ADP
ap-6836	73	18	all	all	DET
ap-6836	73	19	j	j	PROPN
ap-6836	73	20	∈	∈	PROPN
ap-6836	73	21	{	{	PUNCT
ap-6836	73	22	0	0	NUM
ap-6836	73	23	,	,	PUNCT
ap-6836	73	24	1	1	NUM
ap-6836	73	25	,	,	PUNCT
ap-6836	73	26	.	.	PUNCT
ap-6836	73	27	.	.	PUNCT
ap-6836	73	28	.	.	PUNCT
ap-6836	73	29	,	,	PUNCT
ap-6836	73	30	n	n	CCONJ
ap-6836	73	31	}	}	PUNCT
ap-6836	73	32	,	,	PUNCT
ap-6836	73	33	(	(	PUNCT
ap-6836	73	34	1	1	X
ap-6836	73	35	)	)	PUNCT
ap-6836	73	36	(	(	PUNCT
ap-6836	73	37	2	2	NUM
ap-6836	73	38	.	.	PUNCT
ap-6836	73	39	)	)	PUNCT
ap-6836	74	1	an	an	DET
ap-6836	74	2	antipalindromic	antipalindromic	ADJ
ap-6836	74	3	number	number	NOUN
ap-6836	74	4	in	in	ADP
ap-6836	74	5	base	base	PROPN
ap-6836	74	6	b	b	PROPN
ap-6836	74	7	if	if	SCONJ
ap-6836	74	8	its	its	PRON
ap-6836	74	9	digits	digit	NOUN
ap-6836	74	10	satisfy	satisfy	VERB
ap-6836	74	11	the	the	DET
ap-6836	74	12	condition	condition	NOUN
ap-6836	74	13	:	:	PUNCT
ap-6836	74	14	aj	aj	PROPN
ap-6836	74	15	=	=	PROPN
ap-6836	74	16	b−	b−	PROPN
ap-6836	74	17	1−	1−	NUM
ap-6836	74	18	an−j	an−j	ADV
ap-6836	74	19	for	for	ADP
ap-6836	74	20	all	all	DET
ap-6836	74	21	j	j	PROPN
ap-6836	74	22	∈	∈	PROPN
ap-6836	74	23	{	{	PUNCT
ap-6836	74	24	0	0	NUM
ap-6836	74	25	,	,	PUNCT
ap-6836	74	26	1	1	NUM
ap-6836	74	27	,	,	PUNCT
ap-6836	74	28	.	.	PUNCT
ap-6836	74	29	.	.	PUNCT
ap-6836	74	30	.	.	PUNCT
ap-6836	74	31	,	,	PUNCT
ap-6836	74	32	n	n	CCONJ
ap-6836	74	33	}	}	PUNCT
ap-6836	74	34	.	.	PUNCT
ap-6836	75	1	(	(	PUNCT
ap-6836	75	2	2	2	X
ap-6836	75	3	)	)	PUNCT
ap-6836	75	4	the	the	DET
ap-6836	75	5	length	length	NOUN
ap-6836	75	6	of	of	ADP
ap-6836	75	7	the	the	DET
ap-6836	75	8	expansion	expansion	NOUN
ap-6836	75	9	of	of	ADP
ap-6836	75	10	the	the	DET
ap-6836	75	11	number	number	NOUN
ap-6836	75	12	m	m	VERB
ap-6836	75	13	is	be	AUX
ap-6836	75	14	usually	usually	ADV
ap-6836	75	15	denoted	denote	VERB
ap-6836	75	16	|m|	|m|	PROPN
ap-6836	75	17	.	.	PUNCT
ap-6836	75	18	example	example	NOUN
ap-6836	75	19	1	1	NUM
ap-6836	75	20	.	.	X
ap-6836	75	21	consider	consider	VERB
ap-6836	75	22	distinct	distinct	ADJ
ap-6836	75	23	bases	basis	NOUN
ap-6836	75	24	b	b	NOUN
ap-6836	75	25	and	and	CCONJ
ap-6836	75	26	have	have	VERB
ap-6836	75	27	a	a	DET
ap-6836	75	28	look	look	NOUN
ap-6836	75	29	at	at	ADP
ap-6836	75	30	antipalindromic	antipalindromic	ADJ
ap-6836	75	31	numbers	number	NOUN
ap-6836	75	32	in	in	ADP
ap-6836	75	33	these	these	DET
ap-6836	75	34	bases	basis	NOUN
ap-6836	75	35	:	:	PUNCT
ap-6836	76	1	•	•	NUM
ap-6836	76	2	395406	395406	NUM
ap-6836	76	3	is	be	AUX
ap-6836	76	4	an	an	DET
ap-6836	76	5	antipalindromic	antipalindromic	ADJ
ap-6836	76	6	number	number	NOUN
ap-6836	76	7	in	in	ADP
ap-6836	76	8	base	base	PROPN
ap-6836	76	9	b	b	NOUN
ap-6836	76	10	=	=	SYM
ap-6836	76	11	10	10	NUM
ap-6836	76	12	.	.	NOUN
ap-6836	77	1	•	•	NUM
ap-6836	77	2	(	(	PUNCT
ap-6836	77	3	1581)3	1581)3	NUM
ap-6836	77	4	=	=	SYM
ap-6836	77	5	2011120	2011120	NUM
ap-6836	77	6	,	,	PUNCT
ap-6836	77	7	i.e.	i.e.	X
ap-6836	77	8	,	,	PUNCT
ap-6836	77	9	1581	1581	NUM
ap-6836	77	10	is	be	AUX
ap-6836	77	11	an	an	DET
ap-6836	77	12	antipalindromic	antipalindromic	ADJ
ap-6836	77	13	number	number	NOUN
ap-6836	77	14	in	in	ADP
ap-6836	77	15	base	base	PROPN
ap-6836	77	16	b	b	PROPN
ap-6836	77	17	=	=	SYM
ap-6836	77	18	3	3	NUM
ap-6836	77	19	.	.	NOUN
ap-6836	77	20	•	•	NUM
ap-6836	77	21	(	(	PUNCT
ap-6836	77	22	52)2	52)2	NUM
ap-6836	77	23	=	=	SYM
ap-6836	77	24	110100	110100	NUM
ap-6836	77	25	,	,	PUNCT
ap-6836	77	26	i.e.	i.e.	X
ap-6836	77	27	,	,	PUNCT
ap-6836	77	28	52	52	NUM
ap-6836	77	29	is	be	AUX
ap-6836	77	30	an	an	DET
ap-6836	77	31	antipalindromic	antipalindromic	ADJ
ap-6836	77	32	number	number	NOUN
ap-6836	77	33	in	in	ADP
ap-6836	77	34	base	base	PROPN
ap-6836	77	35	b	b	NOUN
ap-6836	77	36	=	=	SYM
ap-6836	77	37	2	2	NUM
ap-6836	77	38	.	.	PUNCT
ap-6836	77	39	observation	observation	NOUN
ap-6836	77	40	1	1	NUM
ap-6836	77	41	.	.	PUNCT
ap-6836	78	1	if	if	SCONJ
ap-6836	78	2	an	an	DET
ap-6836	78	3	antipalindromic	antipalindromic	ADJ
ap-6836	78	4	number	number	NOUN
ap-6836	78	5	in	in	ADP
ap-6836	78	6	base	base	PROPN
ap-6836	78	7	b	b	PROPN
ap-6836	78	8	has	have	VERB
ap-6836	78	9	an	an	DET
ap-6836	78	10	odd	odd	ADJ
ap-6836	78	11	number	number	NOUN
ap-6836	78	12	of	of	ADP
ap-6836	78	13	digits	digit	NOUN
ap-6836	78	14	,	,	PUNCT
ap-6836	78	15	then	then	ADV
ap-6836	78	16	b	b	PROPN
ap-6836	78	17	is	be	AUX
ap-6836	78	18	an	an	DET
ap-6836	78	19	odd	odd	ADJ
ap-6836	78	20	number	number	NOUN
ap-6836	78	21	and	and	CCONJ
ap-6836	78	22	the	the	DET
ap-6836	78	23	middle	middle	ADJ
ap-6836	78	24	digit	digit	NOUN
ap-6836	78	25	is	be	AUX
ap-6836	78	26	equal	equal	ADJ
ap-6836	78	27	to	to	ADP
ap-6836	78	28	b−1	b−1	PROPN
ap-6836	78	29	2	2	NUM
ap-6836	78	30	.	.	PUNCT
ap-6836	79	1	proof	proof	NOUN
ap-6836	79	2	.	.	PUNCT
ap-6836	80	1	it	it	PRON
ap-6836	80	2	follows	follow	VERB
ap-6836	80	3	from	from	ADP
ap-6836	80	4	the	the	DET
ap-6836	80	5	definition	definition	NOUN
ap-6836	80	6	that	that	PRON
ap-6836	80	7	twice	twice	DET
ap-6836	80	8	the	the	DET
ap-6836	80	9	middle	middle	ADJ
ap-6836	80	10	digit	digit	NOUN
ap-6836	80	11	is	be	AUX
ap-6836	80	12	equal	equal	ADJ
ap-6836	80	13	to	to	ADP
ap-6836	80	14	b−1	b−1	PROPN
ap-6836	80	15	.	.	PUNCT
ap-6836	81	1	thus	thus	ADV
ap-6836	81	2	,	,	PUNCT
ap-6836	81	3	b	b	PROPN
ap-6836	81	4	is	be	AUX
ap-6836	81	5	an	an	DET
ap-6836	81	6	odd	odd	ADJ
ap-6836	81	7	number	number	NOUN
ap-6836	81	8	and	and	CCONJ
ap-6836	81	9	the	the	DET
ap-6836	81	10	middle	middle	ADJ
ap-6836	81	11	digit	digit	NOUN
ap-6836	81	12	is	be	AUX
ap-6836	81	13	equal	equal	ADJ
ap-6836	81	14	to	to	ADP
ap-6836	81	15	b−1	b−1	PROPN
ap-6836	81	16	2	2	NUM
ap-6836	81	17	.	.	PUNCT
ap-6836	82	1	observation	observation	NOUN
ap-6836	82	2	2	2	NUM
ap-6836	82	3	.	.	PUNCT
ap-6836	83	1	a	a	DET
ap-6836	83	2	number	number	NOUN
ap-6836	83	3	is	be	AUX
ap-6836	83	4	simultaneously	simultaneously	ADV
ap-6836	83	5	palindromic	palindromic	ADJ
ap-6836	83	6	and	and	CCONJ
ap-6836	83	7	antipalindromic	antipalindromic	ADJ
ap-6836	83	8	if	if	SCONJ
ap-6836	83	9	and	and	CCONJ
ap-6836	83	10	only	only	ADV
ap-6836	83	11	if	if	SCONJ
ap-6836	83	12	b	b	NOUN
ap-6836	83	13	is	be	AUX
ap-6836	83	14	an	an	DET
ap-6836	83	15	odd	odd	ADJ
ap-6836	83	16	number	number	NOUN
ap-6836	83	17	and	and	CCONJ
ap-6836	83	18	all	all	DET
ap-6836	83	19	the	the	DET
ap-6836	83	20	digits	digit	NOUN
ap-6836	83	21	are	be	AUX
ap-6836	83	22	equal	equal	ADJ
ap-6836	83	23	to	to	ADP
ap-6836	83	24	b−1	b−1	PROPN
ap-6836	83	25	2	2	NUM
ap-6836	83	26	.	.	PUNCT
ap-6836	84	1	proof	proof	NOUN
ap-6836	84	2	.	.	PUNCT
ap-6836	85	1	consider	consider	VERB
ap-6836	85	2	an	an	DET
ap-6836	85	3	antipalindromic	antipalindromic	ADJ
ap-6836	85	4	number	number	NOUN
ap-6836	85	5	with	with	ADP
ap-6836	85	6	digits	digit	NOUN
ap-6836	85	7	a0	a0	PROPN
ap-6836	85	8	,	,	PUNCT
ap-6836	85	9	a1	a1	PROPN
ap-6836	85	10	,	,	PUNCT
ap-6836	85	11	.	.	PUNCT
ap-6836	85	12	.	.	PUNCT
ap-6836	86	1	.	.	PUNCT
ap-6836	87	1	,	,	PUNCT
ap-6836	87	2	an	an	X
ap-6836	87	3	.	.	NOUN
ap-6836	88	1	for	for	SCONJ
ap-6836	88	2	this	this	DET
ap-6836	88	3	number	number	NOUN
ap-6836	88	4	to	to	PART
ap-6836	88	5	be	be	AUX
ap-6836	88	6	palindromic	palindromic	ADJ
ap-6836	88	7	,	,	PUNCT
ap-6836	88	8	aj	aj	PROPN
ap-6836	88	9	=	=	PRON
ap-6836	88	10	an−j	an−j	ADV
ap-6836	88	11	must	must	AUX
ap-6836	88	12	be	be	AUX
ap-6836	88	13	true	true	ADJ
ap-6836	88	14	for	for	ADP
ap-6836	88	15	each	each	DET
ap-6836	88	16	j	j	PROPN
ap-6836	88	17	∈	∈	PROPN
ap-6836	88	18	{	{	PUNCT
ap-6836	88	19	0	0	NUM
ap-6836	88	20	,	,	PUNCT
ap-6836	88	21	1	1	NUM
ap-6836	88	22	,	,	PUNCT
ap-6836	88	23	.	.	PUNCT
ap-6836	88	24	.	.	PUNCT
ap-6836	89	1	.	.	PUNCT
ap-6836	89	2	,	,	PUNCT
ap-6836	89	3	n	n	CCONJ
ap-6836	89	4	}	}	PUNCT
ap-6836	89	5	.	.	PUNCT
ap-6836	90	1	from	from	ADP
ap-6836	90	2	the	the	DET
ap-6836	90	3	definition	definition	NOUN
ap-6836	90	4	of	of	ADP
ap-6836	90	5	an	an	DET
ap-6836	90	6	antipalindromic	antipalindromic	ADJ
ap-6836	90	7	number	number	NOUN
ap-6836	90	8	,	,	PUNCT
ap-6836	90	9	it	it	PRON
ap-6836	90	10	follows	follow	VERB
ap-6836	90	11	that	that	SCONJ
ap-6836	90	12	aj	aj	PROPN
ap-6836	90	13	+	+	PROPN
ap-6836	90	14	an−j	an−j	ADV
ap-6836	90	15	=	=	SYM
ap-6836	90	16	b	b	NOUN
ap-6836	90	17	−	−	NOUN
ap-6836	90	18	1	1	NUM
ap-6836	90	19	.	.	PUNCT
ap-6836	91	1	for	for	ADP
ap-6836	91	2	each	each	DET
ap-6836	91	3	j	j	PROPN
ap-6836	91	4	∈	∈	PROPN
ap-6836	91	5	{	{	PUNCT
ap-6836	91	6	0	0	NUM
ap-6836	91	7	,	,	PUNCT
ap-6836	91	8	1	1	NUM
ap-6836	91	9	,	,	PUNCT
ap-6836	91	10	.	.	PUNCT
ap-6836	91	11	.	.	PUNCT
ap-6836	91	12	.	.	PUNCT
ap-6836	92	1	,	,	PUNCT
ap-6836	92	2	n	n	CCONJ
ap-6836	92	3	}	}	PUNCT
ap-6836	92	4	,	,	PUNCT
ap-6836	92	5	we	we	PRON
ap-6836	92	6	obtain	obtain	VERB
ap-6836	92	7	aj	aj	PROPN
ap-6836	92	8	=	=	SYM
ap-6836	92	9	b−1	b−1	PROPN
ap-6836	92	10	2	2	NUM
ap-6836	92	11	,	,	PUNCT
ap-6836	92	12	i.e.	i.e.	X
ap-6836	92	13	,	,	PUNCT
ap-6836	92	14	all	all	DET
ap-6836	92	15	digits	digit	NOUN
ap-6836	92	16	are	be	AUX
ap-6836	92	17	equal	equal	ADJ
ap-6836	92	18	to	to	ADP
ap-6836	92	19	b−1	b−1	PROPN
ap-6836	92	20	2	2	NUM
ap-6836	92	21	and	and	CCONJ
ap-6836	92	22	the	the	DET
ap-6836	92	23	base	base	NOUN
ap-6836	92	24	b	b	PROPN
ap-6836	92	25	must	must	AUX
ap-6836	92	26	,	,	PUNCT
ap-6836	92	27	therefore	therefore	ADV
ap-6836	92	28	,	,	PUNCT
ap-6836	92	29	be	be	AUX
ap-6836	92	30	odd	odd	ADJ
ap-6836	92	31	.	.	PUNCT
ap-6836	93	1	the	the	DET
ap-6836	93	2	opposite	opposite	ADJ
ap-6836	93	3	implication	implication	NOUN
ap-6836	93	4	is	be	AUX
ap-6836	93	5	obvious	obvious	ADJ
ap-6836	93	6	.	.	PUNCT
ap-6836	94	1	3	3	X
ap-6836	94	2	.	.	X
ap-6836	94	3	divisibility	divisibility	NOUN
ap-6836	94	4	and	and	CCONJ
ap-6836	94	5	antipalindromic	antipalindromic	ADJ
ap-6836	94	6	primes	prime	NOUN
ap-6836	94	7	let	let	VERB
ap-6836	94	8	us	we	PRON
ap-6836	94	9	first	first	ADV
ap-6836	94	10	study	study	VERB
ap-6836	94	11	the	the	DET
ap-6836	94	12	divisibility	divisibility	NOUN
ap-6836	94	13	of	of	ADP
ap-6836	94	14	antipalindromic	antipalindromic	ADJ
ap-6836	94	15	numbers	number	NOUN
ap-6836	94	16	,	,	PUNCT
ap-6836	94	17	which	which	PRON
ap-6836	94	18	will	will	AUX
ap-6836	94	19	be	be	AUX
ap-6836	94	20	used	use	VERB
ap-6836	94	21	in	in	ADP
ap-6836	94	22	the	the	DET
ap-6836	94	23	sequel	sequel	NOUN
ap-6836	94	24	to	to	PART
ap-6836	94	25	show	show	VERB
ap-6836	94	26	interesting	interesting	ADJ
ap-6836	94	27	results	result	NOUN
ap-6836	94	28	on	on	ADP
ap-6836	94	29	antipalindromic	antipalindromic	ADJ
ap-6836	94	30	primes	prime	NOUN
ap-6836	94	31	.	.	PUNCT
ap-6836	95	1	lemma	lemma	PROPN
ap-6836	95	2	1	1	X
ap-6836	95	3	.	.	PUNCT
ap-6836	96	1	let	let	VERB
ap-6836	96	2	m	m	PRON
ap-6836	96	3	be	be	AUX
ap-6836	96	4	a	a	DET
ap-6836	96	5	natural	natural	ADJ
ap-6836	96	6	number	number	NOUN
ap-6836	96	7	and	and	CCONJ
ap-6836	96	8	its	its	PRON
ap-6836	96	9	expansion	expansion	NOUN
ap-6836	96	10	in	in	ADP
ap-6836	96	11	base	base	PROPN
ap-6836	96	12	b	b	PROPN
ap-6836	96	13	be	be	AUX
ap-6836	96	14	equal	equal	ADJ
ap-6836	96	15	to	to	PART
ap-6836	96	16	anbn	anbn	VERB
ap-6836	96	17	+	+	CCONJ
ap-6836	96	18	an−1bn−1	an−1bn−1	PROPN
ap-6836	96	19	+	+	ADJ
ap-6836	96	20	.	.	PUNCT
ap-6836	96	21	.	.	PUNCT
ap-6836	96	22	.	.	PUNCT
ap-6836	97	1	+	+	CCONJ
ap-6836	97	2	a1b	a1b	PROPN
ap-6836	97	3	+	+	CCONJ
ap-6836	97	4	a0	a0	PROPN
ap-6836	97	5	.	.	PUNCT
ap-6836	98	1	then	then	ADV
ap-6836	98	2	m	m	VERB
ap-6836	98	3	is	be	AUX
ap-6836	98	4	divisible	divisible	ADJ
ap-6836	98	5	by	by	ADP
ap-6836	98	6	b	b	PROPN
ap-6836	98	7	−	−	PROPN
ap-6836	98	8	1	1	NUM
ap-6836	98	9	if	if	SCONJ
ap-6836	98	10	and	and	CCONJ
ap-6836	98	11	only	only	ADV
ap-6836	98	12	if	if	SCONJ
ap-6836	98	13	the	the	DET
ap-6836	98	14	sum	sum	NOUN
ap-6836	98	15	of	of	ADP
ap-6836	98	16	its	its	PRON
ap-6836	98	17	digits	digit	NOUN
ap-6836	98	18	is	be	AUX
ap-6836	98	19	divisible	divisible	ADJ
ap-6836	98	20	by	by	ADP
ap-6836	98	21	b−	b−	PROPN
ap-6836	98	22	1	1	NUM
ap-6836	98	23	,	,	PUNCT
ap-6836	98	24	i.e.	i.e.	X
ap-6836	98	25	,	,	PUNCT
ap-6836	98	26	an	an	DET
ap-6836	98	27	+	+	X
ap-6836	98	28	an−1	an−1	PROPN
ap-6836	98	29	+	+	NOUN
ap-6836	98	30	.	.	PUNCT
ap-6836	98	31	.	.	PUNCT
ap-6836	98	32	.	.	PUNCT
ap-6836	99	1	+	+	CCONJ
ap-6836	99	2	a1	a1	NOUN
ap-6836	99	3	+	+	CCONJ
ap-6836	99	4	a0	a0	PROPN
ap-6836	99	5	≡	≡	PROPN
ap-6836	99	6	0	0	PUNCT
ap-6836	100	1	(	(	PUNCT
ap-6836	100	2	mod	mod	PROPN
ap-6836	100	3	b−	b−	PROPN
ap-6836	100	4	1	1	NUM
ap-6836	100	5	)	)	PUNCT
ap-6836	100	6	.	.	PUNCT
ap-6836	101	1	proof	proof	NOUN
ap-6836	101	2	.	.	PUNCT
ap-6836	102	1	the	the	DET
ap-6836	102	2	statement	statement	NOUN
ap-6836	102	3	follows	follow	VERB
ap-6836	102	4	from	from	ADP
ap-6836	102	5	the	the	DET
ap-6836	102	6	fact	fact	NOUN
ap-6836	102	7	that	that	SCONJ
ap-6836	102	8	bk	bk	VERB
ap-6836	102	9	≡	≡	PROPN
ap-6836	102	10	1	1	NUM
ap-6836	102	11	(	(	PUNCT
ap-6836	102	12	mod	mod	PROPN
ap-6836	102	13	b−	b−	PROPN
ap-6836	102	14	1	1	NUM
ap-6836	102	15	)	)	PUNCT
ap-6836	102	16	for	for	ADP
ap-6836	102	17	any	any	DET
ap-6836	102	18	k	k	PROPN
ap-6836	102	19	∈	∈	PROPN
ap-6836	102	20	n.	n.	PROPN
ap-6836	102	21	theorem	theorem	VERB
ap-6836	102	22	2	2	NUM
ap-6836	102	23	.	.	PUNCT
ap-6836	103	1	any	any	DET
ap-6836	103	2	antipalindromic	antipalindromic	ADJ
ap-6836	103	3	number	number	NOUN
ap-6836	103	4	with	with	ADP
ap-6836	103	5	an	an	DET
ap-6836	103	6	even	even	ADJ
ap-6836	103	7	number	number	NOUN
ap-6836	103	8	of	of	ADP
ap-6836	103	9	digits	digit	NOUN
ap-6836	103	10	in	in	ADP
ap-6836	103	11	base	base	PROPN
ap-6836	103	12	b	b	PROPN
ap-6836	103	13	is	be	AUX
ap-6836	103	14	divisible	divisible	ADJ
ap-6836	103	15	by	by	ADP
ap-6836	103	16	b−	b−	PROPN
ap-6836	103	17	1	1	NUM
ap-6836	103	18	.	.	PROPN
ap-6836	103	19	429	429	NUM
ap-6836	103	20	ľ	ľ	X
ap-6836	103	21	.	.	PUNCT
ap-6836	104	1	dvořáková	dvořáková	PROPN
ap-6836	104	2	,	,	PUNCT
ap-6836	104	3	s.	s.	PROPN
ap-6836	104	4	kruml	kruml	PROPN
ap-6836	104	5	,	,	PUNCT
ap-6836	104	6	d.	d.	PROPN
ap-6836	104	7	ryzák	ryzák	VERB
ap-6836	104	8	acta	acta	PROPN
ap-6836	104	9	polytechnica	polytechnica	PROPN
ap-6836	104	10	proof	proof	NOUN
ap-6836	104	11	.	.	PUNCT
ap-6836	105	1	consider	consider	VERB
ap-6836	105	2	an	an	DET
ap-6836	105	3	antipalindromic	antipalindromic	ADJ
ap-6836	105	4	number	number	NOUN
ap-6836	105	5	m	m	NOUN
ap-6836	105	6	=	=	PUNCT
ap-6836	105	7	anbn	anbn	PROPN
ap-6836	105	8	+	+	CCONJ
ap-6836	105	9	an−1bn−1	an−1bn−1	PROPN
ap-6836	105	10	+	+	ADJ
ap-6836	105	11	.	.	PUNCT
ap-6836	105	12	.	.	PUNCT
ap-6836	105	13	.	.	PUNCT
ap-6836	106	1	+	+	CCONJ
ap-6836	106	2	a1b	a1b	NOUN
ap-6836	106	3	+	+	CCONJ
ap-6836	106	4	a0	a0	NOUN
ap-6836	106	5	for	for	ADP
ap-6836	106	6	an	an	DET
ap-6836	106	7	odd	odd	ADJ
ap-6836	106	8	n.	n.	NOUN
ap-6836	106	9	from	from	ADP
ap-6836	106	10	the	the	DET
ap-6836	106	11	definition	definition	NOUN
ap-6836	106	12	,	,	PUNCT
ap-6836	106	13	it	it	PRON
ap-6836	106	14	is	be	AUX
ap-6836	106	15	true	true	ADJ
ap-6836	106	16	that	that	SCONJ
ap-6836	106	17	aj	aj	PROPN
ap-6836	106	18	+	+	PROPN
ap-6836	106	19	an−j	an−j	ADV
ap-6836	106	20	=	=	SYM
ap-6836	106	21	b	b	NOUN
ap-6836	106	22	−	−	NOUN
ap-6836	106	23	1	1	NUM
ap-6836	106	24	for	for	ADP
ap-6836	106	25	each	each	DET
ap-6836	106	26	j	j	PROPN
ap-6836	106	27	∈	∈	PROPN
ap-6836	106	28	{	{	PUNCT
ap-6836	106	29	0	0	NUM
ap-6836	106	30	,	,	PUNCT
ap-6836	106	31	1	1	NUM
ap-6836	106	32	,	,	PUNCT
ap-6836	106	33	.	.	PUNCT
ap-6836	106	34	.	.	PUNCT
ap-6836	107	1	.	.	PUNCT
ap-6836	107	2	,	,	PUNCT
ap-6836	107	3	n	n	CCONJ
ap-6836	107	4	}	}	PUNCT
ap-6836	107	5	.	.	PUNCT
ap-6836	108	1	the	the	DET
ap-6836	108	2	number	number	NOUN
ap-6836	108	3	of	of	ADP
ap-6836	108	4	digits	digit	NOUN
ap-6836	108	5	is	be	AUX
ap-6836	108	6	even	even	ADV
ap-6836	108	7	,	,	PUNCT
ap-6836	108	8	hence	hence	ADV
ap-6836	108	9	an+an−1	an+an−1	PROPN
ap-6836	108	10	+	+	PROPN
ap-6836	108	11	.	.	PUNCT
ap-6836	108	12	.	.	PUNCT
ap-6836	108	13	.+a1+a0	.+a1+a0	PROPN
ap-6836	109	1	=	=	PUNCT
ap-6836	110	1	(	(	PUNCT
ap-6836	110	2	b−1)n	b−1)n	NOUN
ap-6836	110	3	+	+	CCONJ
ap-6836	110	4	1	1	NUM
ap-6836	110	5	2	2	NUM
ap-6836	110	6	≡	≡	PROPN
ap-6836	110	7	0	0	PUNCT
ap-6836	110	8	(	(	PUNCT
ap-6836	110	9	mod	mod	PROPN
ap-6836	110	10	b−1	b−1	PROPN
ap-6836	110	11	)	)	PUNCT
ap-6836	110	12	.	.	PUNCT
ap-6836	111	1	using	use	VERB
ap-6836	111	2	lemma	lemma	PROPN
ap-6836	111	3	1	1	NUM
ap-6836	111	4	,	,	PUNCT
ap-6836	111	5	the	the	DET
ap-6836	111	6	antipalindromic	antipalindromic	ADJ
ap-6836	111	7	number	number	NOUN
ap-6836	111	8	m	m	VERB
ap-6836	111	9	is	be	AUX
ap-6836	111	10	divisible	divisible	ADJ
ap-6836	111	11	by	by	ADP
ap-6836	111	12	the	the	DET
ap-6836	111	13	number	number	NOUN
ap-6836	111	14	b−	b−	PROPN
ap-6836	111	15	1	1	NUM
ap-6836	111	16	.	.	PUNCT
ap-6836	112	1	theorem	theorem	NOUN
ap-6836	112	2	3	3	NUM
ap-6836	112	3	.	.	PUNCT
ap-6836	113	1	an	an	DET
ap-6836	113	2	antipalindromic	antipalindromic	ADJ
ap-6836	113	3	number	number	NOUN
ap-6836	113	4	with	with	ADP
ap-6836	113	5	an	an	DET
ap-6836	113	6	odd	odd	ADJ
ap-6836	113	7	number	number	NOUN
ap-6836	113	8	of	of	ADP
ap-6836	113	9	digits	digit	NOUN
ap-6836	113	10	in	in	ADP
ap-6836	113	11	base	base	PROPN
ap-6836	113	12	b	b	PROPN
ap-6836	113	13	is	be	AUX
ap-6836	113	14	divisible	divisible	ADJ
ap-6836	113	15	by	by	ADP
ap-6836	113	16	b−1	b−1	PROPN
ap-6836	113	17	2	2	NUM
ap-6836	113	18	.	.	PUNCT
ap-6836	114	1	proof	proof	NOUN
ap-6836	114	2	.	.	PUNCT
ap-6836	115	1	consider	consider	VERB
ap-6836	115	2	the	the	DET
ap-6836	115	3	antipalindromic	antipalindromic	ADJ
ap-6836	115	4	number	number	NOUN
ap-6836	115	5	m	m	NOUN
ap-6836	115	6	=	=	SYM
ap-6836	115	7	a2nb2n	a2nb2n	X
ap-6836	115	8	+	+	X
ap-6836	115	9	a2n−1b2n−1	a2n−1b2n−1	ADJ
ap-6836	115	10	+	+	X
ap-6836	115	11	.	.	PUNCT
ap-6836	115	12	.	.	PUNCT
ap-6836	115	13	.	.	PUNCT
ap-6836	116	1	+	+	CCONJ
ap-6836	116	2	a1b	a1b	PROPN
ap-6836	116	3	+	+	CCONJ
ap-6836	116	4	a0	a0	PROPN
ap-6836	116	5	.	.	PUNCT
ap-6836	117	1	the	the	DET
ap-6836	117	2	digit	digit	NOUN
ap-6836	117	3	sum	sum	NOUN
ap-6836	117	4	of	of	ADP
ap-6836	117	5	the	the	DET
ap-6836	117	6	number	number	NOUN
ap-6836	117	7	m−	m−	PROPN
ap-6836	117	8	anbn	anbn	PROPN
ap-6836	117	9	is	be	AUX
ap-6836	117	10	divisible	divisible	ADJ
ap-6836	117	11	by	by	ADP
ap-6836	117	12	b−	b−	PROPN
ap-6836	117	13	1	1	NUM
ap-6836	117	14	.	.	PUNCT
ap-6836	117	15	from	from	ADP
ap-6836	117	16	lemma	lemma	PROPN
ap-6836	117	17	1	1	NUM
ap-6836	117	18	,	,	PUNCT
ap-6836	117	19	we	we	PRON
ap-6836	117	20	also	also	ADV
ap-6836	117	21	know	know	VERB
ap-6836	117	22	that	that	SCONJ
ap-6836	117	23	the	the	DET
ap-6836	117	24	number	number	NOUN
ap-6836	117	25	m−	m−	PROPN
ap-6836	117	26	anbn	anbn	PROPN
ap-6836	117	27	itself	itself	PRON
ap-6836	117	28	is	be	AUX
ap-6836	117	29	divisible	divisible	ADJ
ap-6836	117	30	by	by	ADP
ap-6836	117	31	b−	b−	PROPN
ap-6836	117	32	1	1	NUM
ap-6836	117	33	and	and	CCONJ
ap-6836	117	34	,	,	PUNCT
ap-6836	117	35	therefore	therefore	ADV
ap-6836	117	36	,	,	PUNCT
ap-6836	117	37	by	by	ADP
ap-6836	117	38	b−1	b−1	PROPN
ap-6836	117	39	2	2	NUM
ap-6836	117	40	.	.	PUNCT
ap-6836	118	1	from	from	ADP
ap-6836	118	2	observation	observation	NOUN
ap-6836	118	3	1	1	NUM
ap-6836	118	4	,	,	PUNCT
ap-6836	118	5	an	an	DET
ap-6836	118	6	=	=	ADJ
ap-6836	118	7	b−1	b−1	NOUN
ap-6836	118	8	2	2	NUM
ap-6836	118	9	.	.	PUNCT
ap-6836	119	1	the	the	DET
ap-6836	119	2	number	number	NOUN
ap-6836	119	3	m	m	VERB
ap-6836	119	4	is	be	AUX
ap-6836	119	5	a	a	DET
ap-6836	119	6	sum	sum	NOUN
ap-6836	119	7	of	of	ADP
ap-6836	119	8	two	two	NUM
ap-6836	119	9	numbers	number	NOUN
ap-6836	119	10	divisible	divisible	ADJ
ap-6836	119	11	by	by	ADP
ap-6836	119	12	b−1	b−1	PROPN
ap-6836	119	13	2	2	NUM
ap-6836	119	14	.	.	PUNCT
ap-6836	120	1	let	let	VERB
ap-6836	120	2	us	we	PRON
ap-6836	120	3	now	now	ADV
ap-6836	120	4	turn	turn	VERB
ap-6836	120	5	our	our	PRON
ap-6836	120	6	attention	attention	NOUN
ap-6836	120	7	to	to	ADP
ap-6836	120	8	antipalindromic	antipalindromic	ADJ
ap-6836	120	9	primes	prime	NOUN
ap-6836	120	10	.	.	PUNCT
ap-6836	121	1	while	while	SCONJ
ap-6836	121	2	palindromic	palindromic	ADJ
ap-6836	121	3	primes	prime	NOUN
ap-6836	121	4	occur	occur	VERB
ap-6836	121	5	in	in	ADP
ap-6836	121	6	various	various	ADJ
ap-6836	121	7	bases	basis	NOUN
ap-6836	121	8	,	,	PUNCT
ap-6836	121	9	antipalindromic	antipalindromic	ADJ
ap-6836	121	10	primes	prime	NOUN
ap-6836	121	11	occur	occur	VERB
ap-6836	121	12	(	(	PUNCT
ap-6836	121	13	except	except	SCONJ
ap-6836	121	14	some	some	DET
ap-6836	121	15	trivial	trivial	ADJ
ap-6836	121	16	cases	case	NOUN
ap-6836	121	17	)	)	PUNCT
ap-6836	121	18	only	only	ADV
ap-6836	121	19	in	in	ADP
ap-6836	121	20	base	base	NOUN
ap-6836	121	21	3	3	NUM
ap-6836	121	22	.	.	PUNCT
ap-6836	121	23	theorem	theorem	NOUN
ap-6836	121	24	4	4	NUM
ap-6836	121	25	.	.	PUNCT
ap-6836	122	1	let	let	VERB
ap-6836	122	2	base	base	PROPN
ap-6836	122	3	b	b	PROPN
ap-6836	122	4	>	>	X
ap-6836	122	5	3	3	X
ap-6836	122	6	.	.	PUNCT
ap-6836	123	1	then	then	ADV
ap-6836	123	2	there	there	PRON
ap-6836	123	3	exists	exist	VERB
ap-6836	123	4	at	at	ADP
ap-6836	123	5	most	most	ADV
ap-6836	123	6	one	one	NUM
ap-6836	123	7	antipalindromic	antipalindromic	ADJ
ap-6836	123	8	prime	prime	ADJ
ap-6836	123	9	number	number	NOUN
ap-6836	123	10	p	p	NOUN
ap-6836	123	11	in	in	ADP
ap-6836	123	12	base	base	NOUN
ap-6836	123	13	b	b	NOUN
ap-6836	123	14	:	:	PUNCT
ap-6836	123	15	p	p	X
ap-6836	123	16	=	=	PUNCT
ap-6836	123	17	b−1	b−1	NOUN
ap-6836	123	18	2	2	NUM
ap-6836	123	19	.	.	PUNCT
ap-6836	124	1	proof	proof	NOUN
ap-6836	124	2	.	.	PUNCT
ap-6836	125	1	theorems	theorems	PROPN
ap-6836	125	2	2	2	NUM
ap-6836	125	3	and	and	CCONJ
ap-6836	125	4	3	3	NUM
ap-6836	125	5	show	show	VERB
ap-6836	125	6	that	that	SCONJ
ap-6836	125	7	every	every	DET
ap-6836	125	8	antipalindromic	antipalindromic	ADJ
ap-6836	125	9	number	number	NOUN
ap-6836	125	10	is	be	AUX
ap-6836	125	11	divisible	divisible	ADJ
ap-6836	125	12	either	either	ADV
ap-6836	125	13	by	by	ADP
ap-6836	125	14	b−1	b−1	PROPN
ap-6836	125	15	2	2	NUM
ap-6836	125	16	or	or	CCONJ
ap-6836	125	17	b	b	NOUN
ap-6836	126	1	−	−	NOUN
ap-6836	126	2	1	1	NUM
ap-6836	126	3	.	.	PUNCT
ap-6836	127	1	although	although	SCONJ
ap-6836	127	2	b	b	PROPN
ap-6836	127	3	−	−	NOUN
ap-6836	127	4	1	1	NUM
ap-6836	127	5	may	may	AUX
ap-6836	127	6	be	be	AUX
ap-6836	127	7	a	a	DET
ap-6836	127	8	prime	prime	ADJ
ap-6836	127	9	number	number	NOUN
ap-6836	127	10	,	,	PUNCT
ap-6836	127	11	it	it	PRON
ap-6836	127	12	is	be	AUX
ap-6836	127	13	never	never	ADV
ap-6836	127	14	antipalindromic	antipalindromic	ADJ
ap-6836	127	15	.	.	PUNCT
ap-6836	128	1	theorem	theorem	ADJ
ap-6836	128	2	5	5	NUM
ap-6836	128	3	.	.	PUNCT
ap-6836	129	1	let	let	VERB
ap-6836	129	2	base	base	NOUN
ap-6836	129	3	b	b	NOUN
ap-6836	129	4	=	=	SYM
ap-6836	129	5	2	2	NUM
ap-6836	129	6	.	.	PUNCT
ap-6836	130	1	then	then	ADV
ap-6836	130	2	there	there	PRON
ap-6836	130	3	exists	exist	VERB
ap-6836	130	4	only	only	ADV
ap-6836	130	5	one	one	NUM
ap-6836	130	6	antipalindromic	antipalindromic	ADJ
ap-6836	130	7	number	number	NOUN
ap-6836	130	8	p	p	NOUN
ap-6836	130	9	=	=	NOUN
ap-6836	130	10	2	2	NUM
ap-6836	130	11	,	,	PUNCT
ap-6836	130	12	(	(	PUNCT
ap-6836	130	13	p)2	p)2	NOUN
ap-6836	130	14	=	=	SYM
ap-6836	130	15	10	10	NUM
ap-6836	130	16	.	.	PUNCT
ap-6836	131	1	proof	proof	NOUN
ap-6836	131	2	.	.	PUNCT
ap-6836	132	1	every	every	DET
ap-6836	132	2	antipalindromic	antipalindromic	ADJ
ap-6836	132	3	number	number	NOUN
ap-6836	132	4	in	in	ADP
ap-6836	132	5	base	base	PROPN
ap-6836	132	6	b	b	NOUN
ap-6836	132	7	=	=	SYM
ap-6836	132	8	2	2	NUM
ap-6836	132	9	is	be	AUX
ap-6836	132	10	even	even	ADV
ap-6836	132	11	.	.	PUNCT
ap-6836	133	1	2	2	NUM
ap-6836	133	2	is	be	AUX
ap-6836	133	3	the	the	DET
ap-6836	133	4	only	only	ADJ
ap-6836	133	5	even	even	ADV
ap-6836	133	6	prime	prime	ADJ
ap-6836	133	7	number	number	NOUN
ap-6836	133	8	.	.	PUNCT
ap-6836	134	1	theorem	theorem	VERB
ap-6836	134	2	6	6	NUM
ap-6836	134	3	.	.	PUNCT
ap-6836	135	1	let	let	VERB
ap-6836	135	2	base	base	NOUN
ap-6836	135	3	b	b	NOUN
ap-6836	135	4	=	=	SYM
ap-6836	135	5	3	3	NUM
ap-6836	135	6	.	.	X
ap-6836	136	1	every	every	DET
ap-6836	136	2	antipalindromic	antipalindromic	ADJ
ap-6836	136	3	prime	prime	NOUN
ap-6836	136	4	in	in	ADP
ap-6836	136	5	this	this	DET
ap-6836	136	6	base	base	NOUN
ap-6836	136	7	has	have	VERB
ap-6836	136	8	an	an	DET
ap-6836	136	9	odd	odd	ADJ
ap-6836	136	10	number	number	NOUN
ap-6836	136	11	of	of	ADP
ap-6836	136	12	digits	digit	NOUN
ap-6836	136	13	n	n	PRON
ap-6836	136	14	≥	≥	NOUN
ap-6836	136	15	3	3	NUM
ap-6836	136	16	.	.	PUNCT
ap-6836	137	1	proof	proof	NOUN
ap-6836	137	2	.	.	PUNCT
ap-6836	138	1	from	from	ADP
ap-6836	138	2	theorem	theorem	ADJ
ap-6836	138	3	2	2	NUM
ap-6836	138	4	,	,	PUNCT
ap-6836	138	5	antipalindromic	antipalindromic	ADJ
ap-6836	138	6	numbers	number	NOUN
ap-6836	138	7	with	with	ADP
ap-6836	138	8	an	an	DET
ap-6836	138	9	even	even	ADJ
ap-6836	138	10	number	number	NOUN
ap-6836	138	11	of	of	ADP
ap-6836	138	12	digits	digit	NOUN
ap-6836	138	13	in	in	ADP
ap-6836	138	14	base	base	PROPN
ap-6836	138	15	b	b	NOUN
ap-6836	138	16	=	=	SYM
ap-6836	138	17	3	3	NUM
ap-6836	138	18	are	be	AUX
ap-6836	138	19	even	even	ADV
ap-6836	138	20	.	.	PUNCT
ap-6836	139	1	the	the	DET
ap-6836	139	2	only	only	ADJ
ap-6836	139	3	antipalindromic	antipalindromic	ADJ
ap-6836	139	4	number	number	NOUN
ap-6836	139	5	in	in	ADP
ap-6836	139	6	this	this	DET
ap-6836	139	7	base	base	NOUN
ap-6836	139	8	with	with	ADP
ap-6836	139	9	one	one	NUM
ap-6836	139	10	digit	digit	NOUN
ap-6836	139	11	is	be	AUX
ap-6836	139	12	1	1	NUM
ap-6836	139	13	.	.	PUNCT
ap-6836	140	1	lemma	lemma	PROPN
ap-6836	140	2	7	7	X
ap-6836	140	3	.	.	PUNCT
ap-6836	140	4	antipalindromic	antipalindromic	ADJ
ap-6836	140	5	numbers	number	NOUN
ap-6836	140	6	in	in	ADP
ap-6836	140	7	base	base	PROPN
ap-6836	140	8	b	b	NOUN
ap-6836	140	9	=	=	SYM
ap-6836	140	10	3	3	NUM
ap-6836	140	11	beginning	begin	VERB
ap-6836	140	12	with	with	ADP
ap-6836	140	13	the	the	DET
ap-6836	140	14	digit	digit	NOUN
ap-6836	140	15	2	2	NUM
ap-6836	140	16	are	be	AUX
ap-6836	140	17	divisible	divisible	ADJ
ap-6836	140	18	by	by	ADP
ap-6836	140	19	3	3	NUM
ap-6836	140	20	.	.	PUNCT
ap-6836	140	21	proof	proof	NOUN
ap-6836	140	22	.	.	PUNCT
ap-6836	141	1	consider	consider	VERB
ap-6836	141	2	an	an	DET
ap-6836	141	3	antipalindromic	antipalindromic	ADJ
ap-6836	141	4	number	number	NOUN
ap-6836	141	5	m	m	NOUN
ap-6836	141	6	=	=	SYM
ap-6836	141	7	an3n	an3n	PROPN
ap-6836	141	8	+	+	CCONJ
ap-6836	141	9	an−13n−1	an−13n−1	PUNCT
ap-6836	142	1	+	+	CCONJ
ap-6836	142	2	.	.	PUNCT
ap-6836	142	3	.	.	PUNCT
ap-6836	143	1	.	.	PUNCT
ap-6836	144	1	+	+	CCONJ
ap-6836	144	2	a13	a13	PROPN
ap-6836	144	3	+	+	CCONJ
ap-6836	144	4	a0	a0	NOUN
ap-6836	144	5	,	,	PUNCT
ap-6836	144	6	where	where	SCONJ
ap-6836	144	7	an	an	DET
ap-6836	144	8	=	=	NOUN
ap-6836	144	9	2	2	NUM
ap-6836	144	10	.	.	PUNCT
ap-6836	145	1	the	the	DET
ap-6836	145	2	sum	sum	NOUN
ap-6836	145	3	of	of	ADP
ap-6836	145	4	an	an	DET
ap-6836	145	5	and	and	CCONJ
ap-6836	145	6	a0	a0	NOUN
ap-6836	145	7	need	need	VERB
ap-6836	145	8	to	to	PART
ap-6836	145	9	be	be	AUX
ap-6836	145	10	equal	equal	ADJ
ap-6836	145	11	to	to	ADP
ap-6836	145	12	2	2	NUM
ap-6836	145	13	,	,	PUNCT
ap-6836	145	14	therefore	therefore	ADV
ap-6836	145	15	,	,	PUNCT
ap-6836	145	16	a0	a0	PROPN
ap-6836	145	17	=	=	SYM
ap-6836	145	18	0	0	PROPN
ap-6836	145	19	.	.	PUNCT
ap-6836	146	1	all	all	DET
ap-6836	146	2	the	the	DET
ap-6836	146	3	summands	summand	NOUN
ap-6836	146	4	are	be	AUX
ap-6836	146	5	divisible	divisible	ADJ
ap-6836	146	6	by	by	ADP
ap-6836	146	7	3	3	NUM
ap-6836	146	8	.	.	PUNCT
ap-6836	146	9	theorem	theorem	NOUN
ap-6836	146	10	8	8	NUM
ap-6836	146	11	.	.	PUNCT
ap-6836	147	1	all	all	DET
ap-6836	147	2	antipalindromic	antipalindromic	ADJ
ap-6836	147	3	primes	prime	NOUN
ap-6836	147	4	in	in	ADP
ap-6836	147	5	base	base	PROPN
ap-6836	147	6	b	b	NOUN
ap-6836	147	7	=	=	SYM
ap-6836	147	8	3	3	NUM
ap-6836	147	9	can	can	AUX
ap-6836	147	10	be	be	AUX
ap-6836	147	11	expressed	express	VERB
ap-6836	147	12	as	as	ADP
ap-6836	147	13	6k	6k	NOUN
ap-6836	147	14	+	+	X
ap-6836	147	15	1	1	NUM
ap-6836	147	16	,	,	PUNCT
ap-6836	147	17	where	where	SCONJ
ap-6836	147	18	k	k	PROPN
ap-6836	147	19	∈	∈	PROPN
ap-6836	147	20	n.	n.	NOUN
ap-6836	147	21	proof	proof	NOUN
ap-6836	147	22	.	.	PUNCT
ap-6836	148	1	consider	consider	VERB
ap-6836	148	2	an	an	DET
ap-6836	148	3	antipalindromic	antipalindromic	ADJ
ap-6836	148	4	prime	prime	NOUN
ap-6836	148	5	m	m	NOUN
ap-6836	149	1	=	=	PUNCT
ap-6836	149	2	a2n32n	a2n32n	ADJ
ap-6836	149	3	+	+	PUNCT
ap-6836	149	4	a2n−132n−1	a2n−132n−1	PROPN
ap-6836	149	5	+	+	NUM
ap-6836	149	6	.	.	PUNCT
ap-6836	149	7	.	.	PUNCT
ap-6836	149	8	.	.	PUNCT
ap-6836	150	1	+	+	CCONJ
ap-6836	150	2	a13	a13	PROPN
ap-6836	150	3	+	+	CCONJ
ap-6836	150	4	a0	a0	NOUN
ap-6836	150	5	.	.	PUNCT
ap-6836	151	1	(	(	PUNCT
ap-6836	151	2	the	the	DET
ap-6836	151	3	number	number	NOUN
ap-6836	151	4	of	of	ADP
ap-6836	151	5	digits	digit	NOUN
ap-6836	151	6	must	must	AUX
ap-6836	151	7	be	be	AUX
ap-6836	151	8	odd	odd	ADJ
ap-6836	151	9	.	.	PUNCT
ap-6836	151	10	)	)	PUNCT
ap-6836	151	11	from	from	ADP
ap-6836	151	12	lemma	lemma	PROPN
ap-6836	151	13	7	7	NUM
ap-6836	151	14	,	,	PUNCT
ap-6836	151	15	a0	a0	PROPN
ap-6836	151	16	is	be	AUX
ap-6836	151	17	equal	equal	ADJ
ap-6836	151	18	to	to	ADP
ap-6836	151	19	1	1	NUM
ap-6836	151	20	and	and	CCONJ
ap-6836	151	21	a2n	a2n	ADJ
ap-6836	152	1	=	=	SYM
ap-6836	152	2	1	1	X
ap-6836	152	3	.	.	PUNCT
ap-6836	152	4	let	let	VERB
ap-6836	152	5	us	we	PRON
ap-6836	152	6	pair	pair	VERB
ap-6836	152	7	the	the	DET
ap-6836	152	8	digits	digit	NOUN
ap-6836	152	9	of	of	ADP
ap-6836	152	10	the	the	DET
ap-6836	152	11	antipalindromic	antipalindromic	ADJ
ap-6836	152	12	number	number	NOUN
ap-6836	152	13	m	m	PROPN
ap-6836	152	14	(	(	PUNCT
ap-6836	152	15	except	except	SCONJ
ap-6836	152	16	for	for	ADP
ap-6836	152	17	a2n	a2n	NOUN
ap-6836	152	18	,	,	PUNCT
ap-6836	152	19	an	an	PRON
ap-6836	152	20	,	,	PUNCT
ap-6836	152	21	and	and	CCONJ
ap-6836	152	22	a0	a0	PROPN
ap-6836	152	23	):	):	PUNCT
ap-6836	152	24	a2n−j32n−j	a2n−j32n−j	ADV
ap-6836	153	1	+	+	CCONJ
ap-6836	153	2	aj3j	aj3j	PROPN
ap-6836	153	3	,	,	PUNCT
ap-6836	153	4	j	j	PROPN
ap-6836	153	5	∈	∈	PROPN
ap-6836	153	6	{	{	PUNCT
ap-6836	153	7	1	1	NUM
ap-6836	153	8	,	,	PUNCT
ap-6836	153	9	.	.	PUNCT
ap-6836	153	10	.	.	PUNCT
ap-6836	153	11	.	.	PUNCT
ap-6836	154	1	,	,	PUNCT
ap-6836	154	2	n−	n−	NOUN
ap-6836	154	3	1	1	NUM
ap-6836	154	4	}	}	PUNCT
ap-6836	154	5	.	.	PUNCT
ap-6836	155	1	let	let	VERB
ap-6836	155	2	us	we	PRON
ap-6836	155	3	prove	prove	VERB
ap-6836	155	4	that	that	SCONJ
ap-6836	155	5	for	for	ADP
ap-6836	155	6	each	each	DET
ap-6836	155	7	j	j	PROPN
ap-6836	155	8	∈	∈	PROPN
ap-6836	155	9	{	{	PUNCT
ap-6836	155	10	1	1	NUM
ap-6836	155	11	,	,	PUNCT
ap-6836	155	12	.	.	PUNCT
ap-6836	155	13	.	.	PUNCT
ap-6836	156	1	.	.	PUNCT
ap-6836	157	1	,	,	PUNCT
ap-6836	157	2	n−	n−	NOUN
ap-6836	157	3	1	1	NUM
ap-6836	157	4	}	}	PUNCT
ap-6836	157	5	,	,	PUNCT
ap-6836	157	6	the	the	DET
ap-6836	157	7	following	follow	VERB
ap-6836	157	8	expression	expression	NOUN
ap-6836	157	9	is	be	AUX
ap-6836	157	10	divisible	divisible	ADJ
ap-6836	157	11	by	by	ADP
ap-6836	157	12	6	6	NUM
ap-6836	157	13	3j(a2n−j32n−2j	3j(a2n−j32n−2j	NUM
ap-6836	157	14	+	+	CCONJ
ap-6836	157	15	aj	aj	NOUN
ap-6836	157	16	)	)	PUNCT
ap-6836	157	17	we	we	PRON
ap-6836	157	18	can	can	AUX
ap-6836	157	19	only	only	ADV
ap-6836	157	20	consider	consider	VERB
ap-6836	157	21	three	three	NUM
ap-6836	157	22	possibilities	possibility	NOUN
ap-6836	157	23	:	:	PUNCT
ap-6836	157	24	a2n−j	a2n−j	ADV
ap-6836	157	25	=	=	SYM
ap-6836	157	26	2	2	NUM
ap-6836	157	27	,	,	PUNCT
ap-6836	157	28	aj	aj	PROPN
ap-6836	157	29	=	=	PROPN
ap-6836	157	30	0	0	PROPN
ap-6836	157	31	,	,	PUNCT
ap-6836	157	32	or	or	CCONJ
ap-6836	157	33	a2n−j	a2n−j	X
ap-6836	157	34	=	=	PUNCT
ap-6836	157	35	aj	aj	PROPN
ap-6836	157	36	=	=	PROPN
ap-6836	157	37	1	1	NUM
ap-6836	157	38	,	,	PUNCT
ap-6836	157	39	or	or	CCONJ
ap-6836	157	40	a2n−j	a2n−j	X
ap-6836	157	41	=	=	SYM
ap-6836	157	42	0	0	NUM
ap-6836	157	43	,	,	PUNCT
ap-6836	157	44	aj	aj	PROPN
ap-6836	157	45	=	=	PROPN
ap-6836	157	46	2	2	X
ap-6836	157	47	.	.	PUNCT
ap-6836	158	1	in	in	ADP
ap-6836	158	2	either	either	DET
ap-6836	158	3	case	case	NOUN
ap-6836	158	4	,	,	PUNCT
ap-6836	158	5	the	the	DET
ap-6836	158	6	number	number	NOUN
ap-6836	158	7	in	in	ADP
ap-6836	158	8	question	question	NOUN
ap-6836	158	9	is	be	AUX
ap-6836	158	10	divisible	divisible	ADJ
ap-6836	158	11	by	by	ADP
ap-6836	158	12	6	6	NUM
ap-6836	158	13	because	because	SCONJ
ap-6836	158	14	there	there	PRON
ap-6836	158	15	is	be	VERB
ap-6836	158	16	an	an	DET
ap-6836	158	17	even	even	ADJ
ap-6836	158	18	number	number	NOUN
ap-6836	158	19	inside	inside	ADP
ap-6836	158	20	the	the	DET
ap-6836	158	21	bracket	bracket	NOUN
ap-6836	158	22	.	.	PUNCT
ap-6836	159	1	we	we	PRON
ap-6836	159	2	then	then	ADV
ap-6836	159	3	get	get	VERB
ap-6836	159	4	m	m	VERB
ap-6836	159	5	=	=	PUNCT
ap-6836	159	6	a2n32n	a2n32n	VERB
ap-6836	159	7	+	+	CCONJ
ap-6836	159	8	an3n	an3n	PROPN
ap-6836	159	9	+	+	CCONJ
ap-6836	159	10	a0	a0	NOUN
ap-6836	159	11	+	+	CCONJ
ap-6836	159	12	6	6	NUM
ap-6836	159	13	`	`	PUNCT
ap-6836	159	14	=	=	NOUN
ap-6836	159	15	32n	32n	NOUN
ap-6836	159	16	+	+	SYM
ap-6836	159	17	3n	3n	NUM
ap-6836	159	18	+	+	SYM
ap-6836	159	19	1	1	NUM
ap-6836	159	20	+	+	SYM
ap-6836	159	21	6	6	NUM
ap-6836	159	22	`	`	PUNCT
ap-6836	159	23	=	=	SYM
ap-6836	160	1	3n(3n	3n(3n	NUM
ap-6836	160	2	+	+	NOUN
ap-6836	160	3	1	1	NUM
ap-6836	160	4	)	)	PUNCT
ap-6836	160	5	+	+	CCONJ
ap-6836	160	6	1	1	NUM
ap-6836	160	7	+	+	SYM
ap-6836	160	8	6	6	NUM
ap-6836	160	9	`	`	PUNCT
ap-6836	160	10	for	for	ADP
ap-6836	160	11	some	some	DET
ap-6836	160	12	`	`	PUNCT
ap-6836	160	13	∈	∈	PROPN
ap-6836	160	14	n.	n.	NOUN
ap-6836	160	15	the	the	DET
ap-6836	160	16	first	first	ADJ
ap-6836	160	17	summand	summand	NOUN
ap-6836	160	18	is	be	AUX
ap-6836	160	19	also	also	ADV
ap-6836	160	20	divisible	divisible	ADJ
ap-6836	160	21	by	by	ADP
ap-6836	160	22	6	6	NUM
ap-6836	160	23	,	,	PUNCT
ap-6836	160	24	therefore	therefore	ADV
ap-6836	160	25	m	m	VERB
ap-6836	160	26	can	can	AUX
ap-6836	160	27	indeed	indeed	ADV
ap-6836	160	28	be	be	AUX
ap-6836	160	29	expressed	express	VERB
ap-6836	160	30	as	as	ADP
ap-6836	160	31	6k	6k	NOUN
ap-6836	160	32	+	+	CCONJ
ap-6836	160	33	1	1	NUM
ap-6836	160	34	for	for	ADP
ap-6836	160	35	some	some	DET
ap-6836	160	36	k	k	PROPN
ap-6836	160	37	∈	∈	PROPN
ap-6836	160	38	n.	n.	NOUN
ap-6836	160	39	the	the	DET
ap-6836	160	40	application	application	NOUN
ap-6836	160	41	[	[	X
ap-6836	160	42	9	9	NUM
ap-6836	160	43	]	]	PUNCT
ap-6836	160	44	can	can	AUX
ap-6836	160	45	be	be	AUX
ap-6836	160	46	used	use	VERB
ap-6836	160	47	for	for	ADP
ap-6836	160	48	searching	search	VERB
ap-6836	160	49	antipalindromic	antipalindromic	ADJ
ap-6836	160	50	primes	prime	NOUN
ap-6836	160	51	in	in	ADP
ap-6836	160	52	base	base	NOUN
ap-6836	160	53	3	3	NUM
ap-6836	160	54	.	.	PUNCT
ap-6836	160	55	during	during	ADP
ap-6836	160	56	an	an	DET
ap-6836	160	57	extended	extended	ADJ
ap-6836	160	58	search	search	NOUN
ap-6836	160	59	,	,	PUNCT
ap-6836	160	60	the	the	DET
ap-6836	160	61	first	first	ADJ
ap-6836	160	62	637807	637807	NUM
ap-6836	160	63	antipalindromic	antipalindromic	ADJ
ap-6836	160	64	primes	prime	NOUN
ap-6836	160	65	have	have	AUX
ap-6836	160	66	been	be	AUX
ap-6836	160	67	found	find	VERB
ap-6836	160	68	.	.	PUNCT
ap-6836	161	1	let	let	VERB
ap-6836	161	2	us	we	PRON
ap-6836	161	3	now	now	ADV
ap-6836	161	4	list	list	VERB
ap-6836	161	5	at	at	ADP
ap-6836	161	6	least	least	ADJ
ap-6836	161	7	the	the	DET
ap-6836	161	8	first	first	ADJ
ap-6836	161	9	10	10	NUM
ap-6836	161	10	of	of	ADP
ap-6836	161	11	them	they	PRON
ap-6836	161	12	,	,	PUNCT
ap-6836	161	13	along	along	ADP
ap-6836	161	14	with	with	ADP
ap-6836	161	15	their	their	PRON
ap-6836	161	16	expansions	expansion	NOUN
ap-6836	161	17	in	in	ADP
ap-6836	161	18	base	base	NOUN
ap-6836	161	19	3	3	NUM
ap-6836	161	20	:	:	SYM
ap-6836	161	21	13	13	NUM
ap-6836	161	22	111	111	NUM
ap-6836	161	23	97	97	NUM
ap-6836	161	24	10121	10121	NUM
ap-6836	161	25	853	853	NUM
ap-6836	161	26	1011121	1011121	NUM
ap-6836	161	27	1021	1021	NUM
ap-6836	161	28	1101211	1101211	NUM
ap-6836	161	29	1093	1093	NUM
ap-6836	161	30	1111111	1111111	NUM
ap-6836	161	31	7873	7873	NUM
ap-6836	161	32	101210121	101210121	NUM
ap-6836	161	33	8161	8161	NUM
ap-6836	161	34	102012021	102012021	NUM
ap-6836	161	35	8377	8377	NUM
ap-6836	161	36	102111021	102111021	NUM
ap-6836	161	37	9337	9337	NUM
ap-6836	161	38	110210211	110210211	NUM
ap-6836	161	39	12241	12241	NUM
ap-6836	161	40	121210101	121210101	NUM
ap-6836	161	41	4	4	NUM
ap-6836	161	42	.	.	PUNCT
ap-6836	162	1	squares	square	NOUN
ap-6836	162	2	and	and	CCONJ
ap-6836	162	3	other	other	ADJ
ap-6836	162	4	powers	power	NOUN
ap-6836	162	5	as	as	ADP
ap-6836	162	6	antipalindromes	antipalindrome	NOUN
ap-6836	162	7	for	for	ADP
ap-6836	162	8	palindromic	palindromic	ADJ
ap-6836	162	9	numbers	number	NOUN
ap-6836	162	10	,	,	PUNCT
ap-6836	162	11	squares	square	NOUN
ap-6836	162	12	and	and	CCONJ
ap-6836	162	13	higher	high	ADJ
ap-6836	162	14	powers	power	NOUN
ap-6836	162	15	were	be	AUX
ap-6836	162	16	considered	consider	VERB
ap-6836	162	17	in	in	ADP
ap-6836	162	18	[	[	X
ap-6836	162	19	4	4	NUM
ap-6836	162	20	,	,	PUNCT
ap-6836	162	21	5	5	NUM
ap-6836	162	22	]	]	PUNCT
ap-6836	162	23	by	by	ADP
ap-6836	162	24	simmons	simmon	NOUN
ap-6836	162	25	more	more	ADJ
ap-6836	162	26	than	than	ADP
ap-6836	162	27	thirty	thirty	NUM
ap-6836	162	28	years	year	NOUN
ap-6836	162	29	ago	ago	ADV
ap-6836	162	30	.	.	PUNCT
ap-6836	163	1	he	he	PRON
ap-6836	163	2	proved	prove	VERB
ap-6836	163	3	that	that	SCONJ
ap-6836	163	4	there	there	PRON
ap-6836	163	5	were	be	VERB
ap-6836	163	6	infinitely	infinitely	ADV
ap-6836	163	7	many	many	ADJ
ap-6836	163	8	palindromic	palindromic	ADJ
ap-6836	163	9	squares	square	NOUN
ap-6836	163	10	,	,	PUNCT
ap-6836	163	11	cubes	cube	NOUN
ap-6836	163	12	,	,	PUNCT
ap-6836	163	13	and	and	CCONJ
ap-6836	163	14	biquadrates	biquadrate	NOUN
ap-6836	163	15	.	.	PUNCT
ap-6836	164	1	however	however	ADV
ap-6836	164	2	,	,	PUNCT
ap-6836	164	3	his	his	PRON
ap-6836	164	4	conjecture	conjecture	NOUN
ap-6836	164	5	was	be	AUX
ap-6836	164	6	that	that	PRON
ap-6836	164	7	for	for	ADP
ap-6836	164	8	k	k	PROPN
ap-6836	164	9	>	>	X
ap-6836	164	10	4	4	NUM
ap-6836	164	11	,	,	PUNCT
ap-6836	164	12	k	k	PROPN
ap-6836	164	13	∈	∈	PROPN
ap-6836	164	14	n	n	CCONJ
ap-6836	164	15	,	,	PUNCT
ap-6836	164	16	no	no	DET
ap-6836	164	17	integer	integer	NOUN
ap-6836	164	18	m	m	VERB
ap-6836	164	19	exists	exist	VERB
ap-6836	164	20	such	such	ADJ
ap-6836	164	21	that	that	SCONJ
ap-6836	164	22	mk	mk	PROPN
ap-6836	164	23	is	be	AUX
ap-6836	164	24	a	a	DET
ap-6836	164	25	palindromic	palindromic	ADJ
ap-6836	164	26	number	number	NOUN
ap-6836	164	27	(	(	PUNCT
ap-6836	164	28	in	in	ADP
ap-6836	164	29	the	the	DET
ap-6836	164	30	decimal	decimal	ADJ
ap-6836	164	31	base	base	NOUN
ap-6836	164	32	)	)	PUNCT
ap-6836	164	33	.	.	PUNCT
ap-6836	165	1	this	this	DET
ap-6836	165	2	conjecture	conjecture	NOUN
ap-6836	165	3	is	be	AUX
ap-6836	165	4	still	still	ADV
ap-6836	165	5	open	open	ADJ
ap-6836	165	6	.	.	PUNCT
ap-6836	166	1	that	that	PRON
ap-6836	166	2	is	be	AUX
ap-6836	166	3	definitely	definitely	ADV
ap-6836	166	4	not	not	PART
ap-6836	166	5	the	the	DET
ap-6836	166	6	case	case	NOUN
ap-6836	166	7	for	for	ADP
ap-6836	166	8	antipalindromic	antipalindromic	ADJ
ap-6836	166	9	numbers	number	NOUN
ap-6836	166	10	as	as	ADP
ap-6836	166	11	37	37	NUM
ap-6836	166	12	=	=	SYM
ap-6836	166	13	2187	2187	NUM
ap-6836	166	14	is	be	AUX
ap-6836	166	15	antipalindromic	antipalindromic	ADJ
ap-6836	166	16	in	in	ADP
ap-6836	166	17	base	base	NOUN
ap-6836	166	18	10	10	NUM
ap-6836	166	19	.	.	PUNCT
ap-6836	167	1	for	for	ADP
ap-6836	167	2	a	a	DET
ap-6836	167	3	more	more	ADV
ap-6836	167	4	recent	recent	ADJ
ap-6836	167	5	study	study	NOUN
ap-6836	167	6	of	of	ADP
ap-6836	167	7	palindromic	palindromic	ADJ
ap-6836	167	8	powers	power	NOUN
ap-6836	167	9	,	,	PUNCT
ap-6836	167	10	see	see	VERB
ap-6836	167	11	[	[	X
ap-6836	167	12	10	10	NUM
ap-6836	167	13	]	]	PUNCT
ap-6836	167	14	.	.	PUNCT
ap-6836	168	1	let	let	VERB
ap-6836	168	2	us	we	PRON
ap-6836	168	3	answer	answer	VERB
ap-6836	168	4	the	the	DET
ap-6836	168	5	following	follow	VERB
ap-6836	168	6	question	question	NOUN
ap-6836	168	7	:	:	PUNCT
ap-6836	168	8	430	430	NUM
ap-6836	168	9	vol	vol	NOUN
ap-6836	168	10	.	.	PUNCT
ap-6836	169	1	61	61	NUM
ap-6836	169	2	no	no	NOUN
ap-6836	169	3	.	.	PUNCT
ap-6836	170	1	3/2021	3/2021	NUM
ap-6836	170	2	antipalindromic	antipalindromic	ADJ
ap-6836	170	3	numbers	number	NOUN
ap-6836	170	4	base	base	VERB
ap-6836	170	5	n=20	n=20	PROPN
ap-6836	170	6	21	21	NUM
ap-6836	170	7	22	22	NUM
ap-6836	170	8	23	23	NUM
ap-6836	170	9	24	24	NUM
ap-6836	170	10	25	25	NUM
ap-6836	170	11	n2	n2	NOUN
ap-6836	170	12	3	3	NUM
ap-6836	170	13	13	13	NUM
ap-6836	170	14	3	3	NUM
ap-6836	170	15	14	14	NUM
ap-6836	170	16	9	9	NUM
ap-6836	170	17	11	11	NUM
ap-6836	170	18	n2	n2	NOUN
ap-6836	170	19	+	+	CCONJ
ap-6836	170	20	1	1	NUM
ap-6836	170	21	47	47	NUM
ap-6836	170	22	44	44	NUM
ap-6836	170	23	48	48	NUM
ap-6836	170	24	53	53	NUM
ap-6836	170	25	55	55	NUM
ap-6836	170	26	57	57	NUM
ap-6836	170	27	n2	n2	NOUN
ap-6836	170	28	+	+	CCONJ
ap-6836	170	29	2	2	NUM
ap-6836	170	30	2	2	NUM
ap-6836	170	31	2	2	NUM
ap-6836	170	32	2	2	NUM
ap-6836	170	33	2	2	NUM
ap-6836	170	34	2	2	NUM
ap-6836	170	35	1	1	NUM
ap-6836	170	36	table	table	NOUN
ap-6836	170	37	1	1	NUM
ap-6836	170	38	.	.	PUNCT
ap-6836	170	39	number	number	NOUN
ap-6836	170	40	of	of	ADP
ap-6836	170	41	antipalindromic	antipalindromic	ADJ
ap-6836	170	42	squares	square	NOUN
ap-6836	170	43	smaller	small	ADJ
ap-6836	170	44	than	than	ADP
ap-6836	170	45	1012	1012	NUM
ap-6836	170	46	in	in	ADP
ap-6836	170	47	particular	particular	ADJ
ap-6836	170	48	bases	basis	NOUN
ap-6836	170	49	base	base	NOUN
ap-6836	170	50	n=4	n=4	SYM
ap-6836	170	51	5	5	NUM
ap-6836	170	52	6	6	NUM
ap-6836	170	53	7	7	NUM
ap-6836	170	54	8	8	NUM
ap-6836	170	55	9	9	NUM
ap-6836	170	56	10	10	NUM
ap-6836	170	57	11	11	NUM
ap-6836	170	58	12	12	NUM
ap-6836	170	59	n4	n4	PROPN
ap-6836	170	60	0	0	NUM
ap-6836	171	1	1	1	NUM
ap-6836	171	2	0	0	NUM
ap-6836	171	3	1	1	NUM
ap-6836	171	4	0	0	NUM
ap-6836	171	5	1	1	NUM
ap-6836	171	6	0	0	NUM
ap-6836	171	7	0	0	NUM
ap-6836	171	8	0	0	NUM
ap-6836	171	9	n4	n4	PROPN
ap-6836	171	10	+	+	CCONJ
ap-6836	171	11	1	1	NUM
ap-6836	171	12	6	6	NUM
ap-6836	171	13	6	6	NUM
ap-6836	171	14	8	8	NUM
ap-6836	171	15	10	10	NUM
ap-6836	171	16	13	13	NUM
ap-6836	171	17	13	13	NUM
ap-6836	171	18	13	13	NUM
ap-6836	171	19	13	13	NUM
ap-6836	171	20	13	13	NUM
ap-6836	171	21	n4	n4	PROPN
ap-6836	171	22	+	+	CCONJ
ap-6836	171	23	2	2	NUM
ap-6836	171	24	0	0	NUM
ap-6836	171	25	0	0	NUM
ap-6836	171	26	0	0	NUM
ap-6836	171	27	0	0	NUM
ap-6836	171	28	0	0	NUM
ap-6836	171	29	0	0	NUM
ap-6836	171	30	0	0	NUM
ap-6836	171	31	0	0	NUM
ap-6836	171	32	0	0	NUM
ap-6836	171	33	table	table	NOUN
ap-6836	171	34	2	2	NUM
ap-6836	171	35	.	.	X
ap-6836	171	36	number	number	NOUN
ap-6836	171	37	of	of	ADP
ap-6836	171	38	antipalindromic	antipalindromic	ADJ
ap-6836	171	39	biquadrates	biquadrate	NOUN
ap-6836	171	40	smaller	small	ADJ
ap-6836	171	41	than	than	ADP
ap-6836	171	42	1015	1015	NUM
ap-6836	171	43	in	in	ADP
ap-6836	171	44	particular	particular	ADJ
ap-6836	171	45	bases	basis	NOUN
ap-6836	171	46	question	question	VERB
ap-6836	171	47	1	1	NUM
ap-6836	171	48	.	.	X
ap-6836	171	49	are	be	AUX
ap-6836	171	50	there	there	PRON
ap-6836	171	51	any	any	DET
ap-6836	171	52	antipalindromic	antipalindromic	ADJ
ap-6836	171	53	integer	integer	NOUN
ap-6836	171	54	squares	square	NOUN
ap-6836	171	55	?	?	PUNCT
ap-6836	172	1	our	our	PRON
ap-6836	172	2	initial	initial	ADJ
ap-6836	172	3	observation	observation	NOUN
ap-6836	172	4	suggested	suggest	VERB
ap-6836	172	5	that	that	SCONJ
ap-6836	172	6	bases	base	VERB
ap-6836	172	7	b	b	NOUN
ap-6836	172	8	=	=	SYM
ap-6836	172	9	n2	n2	NOUN
ap-6836	172	10	+	+	CCONJ
ap-6836	172	11	1	1	NUM
ap-6836	172	12	,	,	PUNCT
ap-6836	172	13	n	n	PRON
ap-6836	172	14	∈	∈	PROPN
ap-6836	172	15	n	n	CCONJ
ap-6836	172	16	,	,	PUNCT
ap-6836	172	17	have	have	VERB
ap-6836	172	18	the	the	DET
ap-6836	172	19	most	most	ADV
ap-6836	172	20	antipalindromic	antipalindromic	ADJ
ap-6836	172	21	squares	square	NOUN
ap-6836	172	22	and	and	CCONJ
ap-6836	172	23	the	the	DET
ap-6836	172	24	computer	computer	NOUN
ap-6836	172	25	application	application	NOUN
ap-6836	172	26	provided	provide	VERB
ap-6836	172	27	an	an	DET
ap-6836	172	28	additional	additional	ADJ
ap-6836	172	29	insight	insight	NOUN
ap-6836	172	30	needed	need	VERB
ap-6836	172	31	to	to	PART
ap-6836	172	32	prove	prove	VERB
ap-6836	172	33	this	this	DET
ap-6836	172	34	observation	observation	NOUN
ap-6836	172	35	not	not	PART
ap-6836	172	36	only	only	ADV
ap-6836	172	37	for	for	ADP
ap-6836	172	38	squares	square	NOUN
ap-6836	172	39	but	but	CCONJ
ap-6836	172	40	for	for	ADP
ap-6836	172	41	other	other	ADJ
ap-6836	172	42	powers	power	NOUN
ap-6836	172	43	as	as	ADV
ap-6836	172	44	well	well	ADV
ap-6836	172	45	.	.	PUNCT
ap-6836	173	1	table	table	NOUN
ap-6836	173	2	1	1	NUM
ap-6836	173	3	expresses	express	VERB
ap-6836	173	4	the	the	DET
ap-6836	173	5	number	number	NOUN
ap-6836	173	6	of	of	ADP
ap-6836	173	7	antipalindromic	antipalindromic	ADJ
ap-6836	173	8	squares	square	NOUN
ap-6836	173	9	smaller	small	ADJ
ap-6836	173	10	than	than	ADP
ap-6836	173	11	1012	1012	NUM
ap-6836	173	12	in	in	ADP
ap-6836	173	13	bases	basis	NOUN
ap-6836	173	14	n2	n2	ADJ
ap-6836	173	15	,	,	PUNCT
ap-6836	173	16	n2	n2	ADJ
ap-6836	173	17	+	+	CCONJ
ap-6836	173	18	1	1	NUM
ap-6836	173	19	,	,	PUNCT
ap-6836	173	20	and	and	CCONJ
ap-6836	173	21	n2	n2	ADJ
ap-6836	173	22	+	+	CCONJ
ap-6836	173	23	2	2	NUM
ap-6836	173	24	to	to	PART
ap-6836	173	25	underline	underline	VERB
ap-6836	173	26	the	the	DET
ap-6836	173	27	differences	difference	NOUN
ap-6836	173	28	between	between	ADP
ap-6836	173	29	the	the	DET
ap-6836	173	30	bases	basis	NOUN
ap-6836	173	31	of	of	ADP
ap-6836	173	32	the	the	DET
ap-6836	173	33	form	form	NOUN
ap-6836	173	34	n2	n2	NOUN
ap-6836	173	35	+	+	CCONJ
ap-6836	173	36	1	1	NUM
ap-6836	173	37	and	and	CCONJ
ap-6836	173	38	the	the	DET
ap-6836	173	39	others	other	NOUN
ap-6836	173	40	.	.	PUNCT
ap-6836	174	1	as	as	SCONJ
ap-6836	174	2	the	the	DET
ap-6836	174	3	exponent	exponent	NOUN
ap-6836	174	4	of	of	ADP
ap-6836	174	5	nk	nk	PROPN
ap-6836	174	6	is	be	AUX
ap-6836	174	7	raised	raise	VERB
ap-6836	174	8	,	,	PUNCT
ap-6836	174	9	the	the	DET
ap-6836	174	10	differences	difference	NOUN
ap-6836	174	11	between	between	ADP
ap-6836	174	12	the	the	DET
ap-6836	174	13	number	number	NOUN
ap-6836	174	14	of	of	ADP
ap-6836	174	15	antipalindromic	antipalindromic	PROPN
ap-6836	174	16	k	k	NOUN
ap-6836	174	17	-	-	NOUN
ap-6836	174	18	powers	power	NOUN
ap-6836	174	19	in	in	ADP
ap-6836	174	20	the	the	DET
ap-6836	174	21	base	base	NOUN
ap-6836	174	22	nk	nk	PROPN
ap-6836	175	1	+	+	CCONJ
ap-6836	175	2	1	1	NUM
ap-6836	175	3	and	and	CCONJ
ap-6836	175	4	the	the	DET
ap-6836	175	5	others	other	NOUN
ap-6836	175	6	become	become	VERB
ap-6836	175	7	even	even	ADV
ap-6836	175	8	more	more	ADV
ap-6836	175	9	significant	significant	ADJ
ap-6836	175	10	,	,	PUNCT
ap-6836	175	11	but	but	CCONJ
ap-6836	175	12	the	the	DET
ap-6836	175	13	numbers	number	NOUN
ap-6836	175	14	rise	rise	VERB
ap-6836	175	15	faster	fast	ADV
ap-6836	175	16	,	,	PUNCT
ap-6836	175	17	thus	thus	ADV
ap-6836	175	18	we	we	PRON
ap-6836	175	19	meet	meet	VERB
ap-6836	175	20	the	the	DET
ap-6836	175	21	computational	computational	ADJ
ap-6836	175	22	limits	limit	NOUN
ap-6836	175	23	of	of	ADP
ap-6836	175	24	our	our	PRON
ap-6836	175	25	program	program	NOUN
ap-6836	175	26	already	already	ADV
ap-6836	175	27	for	for	ADP
ap-6836	175	28	small	small	ADJ
ap-6836	175	29	values	value	NOUN
ap-6836	175	30	of	of	ADP
ap-6836	175	31	n	n	CCONJ
ap-6836	175	32	,	,	PUNCT
ap-6836	175	33	see	see	VERB
ap-6836	175	34	table	table	NOUN
ap-6836	175	35	2	2	NUM
ap-6836	175	36	.	.	PUNCT
ap-6836	175	37	example	example	NOUN
ap-6836	175	38	2	2	NUM
ap-6836	175	39	.	.	X
ap-6836	175	40	consider	consider	VERB
ap-6836	175	41	the	the	DET
ap-6836	175	42	base	base	NOUN
ap-6836	175	43	b	b	NOUN
ap-6836	175	44	=	=	SYM
ap-6836	175	45	10	10	NUM
ap-6836	175	46	=	=	SYM
ap-6836	175	47	32	32	NUM
ap-6836	175	48	+	+	CCONJ
ap-6836	175	49	1	1	X
ap-6836	175	50	.	.	X
ap-6836	176	1	any	any	DET
ap-6836	176	2	antipalindromic	antipalindromic	ADJ
ap-6836	176	3	number	number	NOUN
ap-6836	176	4	in	in	ADP
ap-6836	176	5	this	this	DET
ap-6836	176	6	base	base	NOUN
ap-6836	176	7	must	must	AUX
ap-6836	176	8	be	be	AUX
ap-6836	176	9	divisible	divisible	ADJ
ap-6836	176	10	by	by	ADP
ap-6836	176	11	9	9	NUM
ap-6836	176	12	.	.	PUNCT
ap-6836	177	1	every	every	DET
ap-6836	177	2	double	double	ADJ
ap-6836	177	3	-	-	PUNCT
ap-6836	177	4	digit	digit	NOUN
ap-6836	177	5	number	number	NOUN
ap-6836	177	6	divisible	divisible	ADJ
ap-6836	177	7	by	by	ADP
ap-6836	177	8	9	9	NUM
ap-6836	177	9	(	(	PUNCT
ap-6836	177	10	except	except	SCONJ
ap-6836	177	11	99	99	NUM
ap-6836	177	12	)	)	PUNCT
ap-6836	177	13	is	be	AUX
ap-6836	177	14	antipalindromic	antipalindromic	ADJ
ap-6836	177	15	:	:	PUNCT
ap-6836	177	16	18	18	NUM
ap-6836	177	17	,	,	PUNCT
ap-6836	177	18	27	27	NUM
ap-6836	177	19	,	,	PUNCT
ap-6836	177	20	36	36	NUM
ap-6836	177	21	,	,	PUNCT
ap-6836	177	22	45	45	NUM
ap-6836	177	23	,	,	PUNCT
ap-6836	177	24	54	54	NUM
ap-6836	177	25	,	,	PUNCT
ap-6836	177	26	63	63	NUM
ap-6836	177	27	,	,	PUNCT
ap-6836	177	28	72	72	NUM
ap-6836	177	29	,	,	PUNCT
ap-6836	177	30	81	81	NUM
ap-6836	177	31	,	,	PUNCT
ap-6836	177	32	90	90	NUM
ap-6836	177	33	.	.	PUNCT
ap-6836	178	1	the	the	DET
ap-6836	178	2	number	number	NOUN
ap-6836	178	3	9	9	NUM
ap-6836	178	4	is	be	AUX
ap-6836	178	5	a	a	DET
ap-6836	178	6	square	square	NOUN
ap-6836	178	7	,	,	PUNCT
ap-6836	178	8	so	so	CCONJ
ap-6836	178	9	if	if	SCONJ
ap-6836	178	10	a	a	DET
ap-6836	178	11	square	square	NOUN
ap-6836	178	12	is	be	AUX
ap-6836	178	13	divided	divide	VERB
ap-6836	178	14	by	by	ADP
ap-6836	178	15	9	9	NUM
ap-6836	178	16	,	,	PUNCT
ap-6836	178	17	it	it	PRON
ap-6836	178	18	is	be	AUX
ap-6836	178	19	still	still	ADV
ap-6836	178	20	a	a	DET
ap-6836	178	21	square	square	NOUN
ap-6836	178	22	.	.	PUNCT
ap-6836	179	1	36	36	NUM
ap-6836	179	2	=	=	SYM
ap-6836	179	3	4	4	NUM
ap-6836	179	4	·	·	SYM
ap-6836	179	5	9	9	NUM
ap-6836	179	6	=	=	SYM
ap-6836	179	7	22	22	NUM
ap-6836	179	8	·	·	SYM
ap-6836	179	9	32	32	NUM
ap-6836	179	10	=	=	SYM
ap-6836	179	11	62	62	NUM
ap-6836	179	12	,	,	PUNCT
ap-6836	179	13	81	81	NUM
ap-6836	179	14	=	=	SYM
ap-6836	179	15	9	9	NUM
ap-6836	179	16	·	·	SYM
ap-6836	179	17	9	9	NUM
ap-6836	179	18	=	=	SYM
ap-6836	179	19	92	92	NUM
ap-6836	179	20	.	.	PUNCT
ap-6836	180	1	thus	thus	ADV
ap-6836	180	2	36	36	NUM
ap-6836	180	3	and	and	CCONJ
ap-6836	180	4	81	81	NUM
ap-6836	180	5	are	be	AUX
ap-6836	180	6	antipalindromic	antipalindromic	ADJ
ap-6836	180	7	squares	square	NOUN
ap-6836	180	8	.	.	PUNCT
ap-6836	181	1	proposition	proposition	NOUN
ap-6836	181	2	1	1	NUM
ap-6836	181	3	.	.	PUNCT
ap-6836	182	1	for	for	ADP
ap-6836	182	2	b	b	NOUN
ap-6836	182	3	=	=	PROPN
ap-6836	182	4	n2	n2	PROPN
ap-6836	182	5	+	+	CCONJ
ap-6836	182	6	1	1	NUM
ap-6836	182	7	,	,	PUNCT
ap-6836	182	8	n	n	PRON
ap-6836	182	9	∈	∈	PROPN
ap-6836	182	10	n	n	CCONJ
ap-6836	182	11	,	,	PUNCT
ap-6836	182	12	and	and	CCONJ
ap-6836	182	13	m	m	PROPN
ap-6836	182	14	∈	∈	NOUN
ap-6836	182	15	{	{	PUNCT
ap-6836	182	16	2	2	NUM
ap-6836	182	17	,	,	PUNCT
ap-6836	182	18	3	3	NUM
ap-6836	182	19	,	,	PUNCT
ap-6836	182	20	.	.	PUNCT
ap-6836	182	21	.	.	PUNCT
ap-6836	182	22	.	.	PUNCT
ap-6836	183	1	,	,	PUNCT
ap-6836	183	2	n	n	CCONJ
ap-6836	183	3	}	}	PUNCT
ap-6836	183	4	,	,	PUNCT
ap-6836	183	5	the	the	DET
ap-6836	183	6	number	number	NOUN
ap-6836	183	7	(	(	PUNCT
ap-6836	183	8	m	m	PROPN
ap-6836	183	9	·	·	PUNCT
ap-6836	183	10	n)2	n)2	NOUN
ap-6836	183	11	is	be	AUX
ap-6836	183	12	antipalindromic	antipalindromic	ADJ
ap-6836	183	13	.	.	PUNCT
ap-6836	184	1	proof	proof	NOUN
ap-6836	184	2	.	.	PUNCT
ap-6836	185	1	since	since	SCONJ
ap-6836	185	2	b	b	PROPN
ap-6836	185	3	=	=	SYM
ap-6836	185	4	n2	n2	PROPN
ap-6836	185	5	+1	+1	PROPN
ap-6836	185	6	,	,	PUNCT
ap-6836	185	7	we	we	PRON
ap-6836	185	8	can	can	AUX
ap-6836	185	9	modify	modify	VERB
ap-6836	185	10	the	the	DET
ap-6836	185	11	expression	expression	NOUN
ap-6836	185	12	as	as	SCONJ
ap-6836	185	13	follows	follow	VERB
ap-6836	185	14	:	:	PUNCT
ap-6836	185	15	(	(	PUNCT
ap-6836	185	16	m	m	PROPN
ap-6836	185	17	·	·	PUNCT
ap-6836	185	18	n)2	n)2	PROPN
ap-6836	185	19	=	=	SYM
ap-6836	185	20	m2	m2	PROPN
ap-6836	185	21	·	·	PUNCT
ap-6836	185	22	(	(	PUNCT
ap-6836	185	23	b−	b−	NOUN
ap-6836	185	24	1	1	NUM
ap-6836	185	25	)	)	PUNCT
ap-6836	185	26	.	.	PUNCT
ap-6836	186	1	this	this	DET
ap-6836	186	2	number	number	NOUN
ap-6836	186	3	has	have	VERB
ap-6836	186	4	the	the	DET
ap-6836	186	5	expansion	expansion	NOUN
ap-6836	186	6	in	in	ADP
ap-6836	186	7	base	base	PROPN
ap-6836	186	8	b	b	PROPN
ap-6836	186	9	equal	equal	ADJ
ap-6836	186	10	to	to	ADP
ap-6836	186	11	(	(	PUNCT
ap-6836	186	12	m2	m2	PROPN
ap-6836	186	13	−	−	PROPN
ap-6836	186	14	1	1	NUM
ap-6836	186	15	)	)	PUNCT
ap-6836	186	16	(	(	PUNCT
ap-6836	186	17	b−m2	b−m2	NOUN
ap-6836	186	18	)	)	PUNCT
ap-6836	186	19	,	,	PUNCT
ap-6836	186	20	hence	hence	ADV
ap-6836	186	21	it	it	PRON
ap-6836	186	22	is	be	AUX
ap-6836	186	23	antipalindromic	antipalindromic	ADJ
ap-6836	186	24	.	.	PUNCT
ap-6836	187	1	further	far	ADV
ap-6836	187	2	on	on	ADV
ap-6836	187	3	,	,	PUNCT
ap-6836	187	4	we	we	PRON
ap-6836	187	5	will	will	AUX
ap-6836	187	6	answer	answer	VERB
ap-6836	187	7	the	the	DET
ap-6836	187	8	following	follow	VERB
ap-6836	187	9	question	question	NOUN
ap-6836	187	10	.	.	PUNCT
ap-6836	188	1	question	question	NOUN
ap-6836	188	2	2	2	NUM
ap-6836	188	3	.	.	X
ap-6836	188	4	are	be	AUX
ap-6836	188	5	there	there	PRON
ap-6836	188	6	any	any	DET
ap-6836	188	7	higher	high	ADJ
ap-6836	188	8	integer	integer	NOUN
ap-6836	188	9	powers	power	NOUN
ap-6836	188	10	that	that	PRON
ap-6836	188	11	are	be	AUX
ap-6836	188	12	also	also	ADV
ap-6836	188	13	antipalindromic	antipalindromic	ADJ
ap-6836	188	14	numbers	number	NOUN
ap-6836	188	15	?	?	PUNCT
ap-6836	188	16	example	example	NOUN
ap-6836	189	1	3	3	X
ap-6836	189	2	.	.	X
ap-6836	189	3	consider	consider	VERB
ap-6836	189	4	the	the	DET
ap-6836	189	5	base	base	NOUN
ap-6836	189	6	b	b	PROPN
ap-6836	189	7	=	=	SYM
ap-6836	189	8	28	28	NUM
ap-6836	189	9	=	=	SYM
ap-6836	189	10	33	33	NUM
ap-6836	190	1	+	+	NOUN
ap-6836	190	2	1	1	NUM
ap-6836	190	3	.	.	X
ap-6836	191	1	any	any	DET
ap-6836	191	2	antipalindromic	antipalindromic	ADJ
ap-6836	191	3	number	number	NOUN
ap-6836	191	4	in	in	ADP
ap-6836	191	5	this	this	DET
ap-6836	191	6	base	base	NOUN
ap-6836	191	7	with	with	ADP
ap-6836	191	8	an	an	DET
ap-6836	191	9	even	even	ADJ
ap-6836	191	10	number	number	NOUN
ap-6836	191	11	of	of	ADP
ap-6836	191	12	digits	digit	NOUN
ap-6836	191	13	must	must	AUX
ap-6836	191	14	be	be	AUX
ap-6836	191	15	divisible	divisible	ADJ
ap-6836	191	16	by	by	ADP
ap-6836	191	17	27	27	NUM
ap-6836	191	18	.	.	PUNCT
ap-6836	192	1	every	every	DET
ap-6836	192	2	double	double	ADJ
ap-6836	192	3	-	-	PUNCT
ap-6836	192	4	digit	digit	NOUN
ap-6836	192	5	number	number	NOUN
ap-6836	192	6	divisible	divisible	ADJ
ap-6836	192	7	by	by	ADP
ap-6836	192	8	27	27	NUM
ap-6836	192	9	(	(	PUNCT
ap-6836	192	10	except	except	SCONJ
ap-6836	192	11	the	the	DET
ap-6836	192	12	one	one	NOUN
ap-6836	192	13	with	with	ADP
ap-6836	192	14	expansion	expansion	NOUN
ap-6836	192	15	(	(	PUNCT
ap-6836	192	16	27)(27	27)(27	NUM
ap-6836	192	17	)	)	PUNCT
ap-6836	192	18	)	)	PUNCT
ap-6836	192	19	is	be	AUX
ap-6836	192	20	antipalindromic	antipalindromic	ADJ
ap-6836	192	21	.	.	PUNCT
ap-6836	193	1	the	the	DET
ap-6836	193	2	number	number	NOUN
ap-6836	193	3	27	27	NUM
ap-6836	193	4	is	be	AUX
ap-6836	193	5	a	a	DET
ap-6836	193	6	third	third	ADJ
ap-6836	193	7	power	power	NOUN
ap-6836	193	8	of	of	ADP
ap-6836	193	9	3	3	NUM
ap-6836	193	10	,	,	PUNCT
ap-6836	193	11	so	so	CCONJ
ap-6836	193	12	if	if	SCONJ
ap-6836	193	13	a	a	DET
ap-6836	193	14	third	third	ADJ
ap-6836	193	15	power	power	NOUN
ap-6836	193	16	of	of	ADP
ap-6836	193	17	any	any	DET
ap-6836	193	18	number	number	NOUN
ap-6836	193	19	is	be	AUX
ap-6836	193	20	divided	divide	VERB
ap-6836	193	21	by	by	ADP
ap-6836	193	22	27	27	NUM
ap-6836	193	23	,	,	PUNCT
ap-6836	193	24	it	it	PRON
ap-6836	193	25	still	still	ADV
ap-6836	193	26	is	be	AUX
ap-6836	193	27	a	a	DET
ap-6836	193	28	third	third	ADJ
ap-6836	193	29	power	power	NOUN
ap-6836	193	30	of	of	ADP
ap-6836	193	31	an	an	DET
ap-6836	193	32	integer	integer	NOUN
ap-6836	193	33	.	.	PUNCT
ap-6836	194	1	(	(	PUNCT
ap-6836	194	2	7)(20	7)(20	NUM
ap-6836	194	3	)	)	PUNCT
ap-6836	194	4	=	=	PUNCT
ap-6836	195	1	(	(	PUNCT
ap-6836	195	2	216)28	216)28	NOUN
ap-6836	195	3	and	and	CCONJ
ap-6836	195	4	216	216	NUM
ap-6836	195	5	=	=	SYM
ap-6836	195	6	8	8	NUM
ap-6836	195	7	·	·	SYM
ap-6836	195	8	27	27	NUM
ap-6836	195	9	=	=	SYM
ap-6836	195	10	23	23	NUM
ap-6836	195	11	·	·	SYM
ap-6836	195	12	33	33	NUM
ap-6836	195	13	=	=	SYM
ap-6836	195	14	63	63	NUM
ap-6836	195	15	,	,	PUNCT
ap-6836	195	16	(	(	PUNCT
ap-6836	195	17	26)(1	26)(1	NOUN
ap-6836	195	18	)	)	PUNCT
ap-6836	195	19	=	=	SYM
ap-6836	195	20	(	(	PUNCT
ap-6836	195	21	729)28	729)28	NOUN
ap-6836	195	22	and	and	CCONJ
ap-6836	195	23	729	729	NUM
ap-6836	195	24	=	=	SYM
ap-6836	195	25	27	27	NUM
ap-6836	195	26	·	·	SYM
ap-6836	195	27	27	27	NUM
ap-6836	195	28	=	=	SYM
ap-6836	195	29	33	33	NUM
ap-6836	195	30	·	·	SYM
ap-6836	195	31	33	33	NUM
ap-6836	195	32	=	=	SYM
ap-6836	195	33	93	93	NUM
ap-6836	195	34	.	.	PUNCT
ap-6836	196	1	thus	thus	ADV
ap-6836	196	2	216	216	NUM
ap-6836	196	3	and	and	CCONJ
ap-6836	196	4	729	729	NUM
ap-6836	196	5	are	be	AUX
ap-6836	196	6	antipalindromic	antipalindromic	ADJ
ap-6836	196	7	cubes	cube	NOUN
ap-6836	196	8	.	.	PUNCT
ap-6836	197	1	theorem	theorem	VERB
ap-6836	197	2	9	9	NUM
ap-6836	197	3	.	.	PUNCT
ap-6836	198	1	for	for	ADP
ap-6836	198	2	b	b	NOUN
ap-6836	198	3	=	=	SYM
ap-6836	198	4	nk	nk	PROPN
ap-6836	198	5	+	+	NOUN
ap-6836	198	6	1	1	NUM
ap-6836	198	7	,	,	PUNCT
ap-6836	198	8	where	where	SCONJ
ap-6836	198	9	n	n	X
ap-6836	198	10	,	,	PUNCT
ap-6836	198	11	k	k	PROPN
ap-6836	198	12	∈	∈	PROPN
ap-6836	198	13	n	n	CCONJ
ap-6836	198	14	,	,	PUNCT
ap-6836	198	15	k	k	X
ap-6836	198	16	≥	≥	NUM
ap-6836	198	17	2	2	NUM
ap-6836	198	18	,	,	PUNCT
ap-6836	198	19	and	and	CCONJ
ap-6836	198	20	m	m	PROPN
ap-6836	198	21	∈	∈	NOUN
ap-6836	198	22	{	{	PUNCT
ap-6836	198	23	2	2	NUM
ap-6836	198	24	,	,	PUNCT
ap-6836	198	25	3	3	NUM
ap-6836	198	26	,	,	PUNCT
ap-6836	198	27	.	.	PUNCT
ap-6836	198	28	.	.	PUNCT
ap-6836	198	29	.	.	PUNCT
ap-6836	199	1	,	,	PUNCT
ap-6836	199	2	n	n	CCONJ
ap-6836	199	3	}	}	PUNCT
ap-6836	199	4	,	,	PUNCT
ap-6836	199	5	the	the	DET
ap-6836	199	6	number	number	NOUN
ap-6836	199	7	(	(	PUNCT
ap-6836	199	8	m·n)k	m·n)k	PROPN
ap-6836	199	9	is	be	AUX
ap-6836	199	10	antipalindromic	antipalindromic	ADJ
ap-6836	199	11	.	.	PUNCT
ap-6836	200	1	proof	proof	NOUN
ap-6836	200	2	.	.	PUNCT
ap-6836	201	1	since	since	SCONJ
ap-6836	201	2	b	b	PROPN
ap-6836	201	3	=	=	SYM
ap-6836	201	4	nk	nk	PROPN
ap-6836	201	5	+1	+1	PROPN
ap-6836	201	6	,	,	PUNCT
ap-6836	201	7	we	we	PRON
ap-6836	201	8	can	can	AUX
ap-6836	201	9	modify	modify	VERB
ap-6836	201	10	the	the	DET
ap-6836	201	11	expression	expression	NOUN
ap-6836	201	12	as	as	SCONJ
ap-6836	201	13	follows	follow	VERB
ap-6836	201	14	:	:	PUNCT
ap-6836	201	15	(	(	PUNCT
ap-6836	201	16	m	m	NOUN
ap-6836	201	17	·	·	PUNCT
ap-6836	201	18	n)k	n)k	X
ap-6836	201	19	=	=	PUNCT
ap-6836	201	20	mk	mk	NOUN
ap-6836	201	21	·	·	PUNCT
ap-6836	201	22	(	(	PUNCT
ap-6836	201	23	b−	b−	NOUN
ap-6836	201	24	1	1	NUM
ap-6836	201	25	)	)	PUNCT
ap-6836	201	26	.	.	PUNCT
ap-6836	202	1	this	this	DET
ap-6836	202	2	number	number	NOUN
ap-6836	202	3	has	have	VERB
ap-6836	202	4	the	the	DET
ap-6836	202	5	expansion	expansion	NOUN
ap-6836	202	6	in	in	ADP
ap-6836	202	7	base	base	PROPN
ap-6836	202	8	b	b	PROPN
ap-6836	202	9	equal	equal	ADJ
ap-6836	202	10	to	to	ADP
ap-6836	202	11	(	(	PUNCT
ap-6836	202	12	mk	mk	PROPN
ap-6836	202	13	−	−	PROPN
ap-6836	202	14	1)(b−mk	1)(b−mk	NUM
ap-6836	202	15	)	)	PUNCT
ap-6836	202	16	,	,	PUNCT
ap-6836	202	17	thus	thus	ADV
ap-6836	202	18	it	it	PRON
ap-6836	202	19	is	be	AUX
ap-6836	202	20	antipalindromic	antipalindromic	ADJ
ap-6836	202	21	.	.	PUNCT
ap-6836	203	1	for	for	ADP
ap-6836	203	2	odd	odd	ADJ
ap-6836	203	3	powers	power	NOUN
ap-6836	203	4	and	and	CCONJ
ap-6836	203	5	high	high	ADJ
ap-6836	203	6	enough	enough	ADJ
ap-6836	203	7	bases	basis	NOUN
ap-6836	203	8	,	,	PUNCT
ap-6836	203	9	other	other	ADJ
ap-6836	203	10	patterns	pattern	NOUN
ap-6836	203	11	exist	exist	VERB
ap-6836	203	12	.	.	PUNCT
ap-6836	204	1	theorem	theorem	VERB
ap-6836	204	2	10	10	NUM
ap-6836	204	3	.	.	PUNCT
ap-6836	205	1	for	for	ADP
ap-6836	205	2	integers	integer	NOUN
ap-6836	205	3	m	m	VERB
ap-6836	205	4	>	>	X
ap-6836	205	5	1	1	NUM
ap-6836	205	6	and	and	CCONJ
ap-6836	205	7	odd	odd	ADJ
ap-6836	205	8	k	k	PROPN
ap-6836	205	9	>	>	X
ap-6836	205	10	1	1	NUM
ap-6836	205	11	,	,	PUNCT
ap-6836	205	12	there	there	PRON
ap-6836	205	13	exists	exist	VERB
ap-6836	205	14	a	a	DET
ap-6836	205	15	number	number	NOUN
ap-6836	205	16	c	c	NOUN
ap-6836	205	17	such	such	ADJ
ap-6836	205	18	that	that	PRON
ap-6836	205	19	in	in	ADP
ap-6836	205	20	every	every	DET
ap-6836	205	21	base	base	NOUN
ap-6836	205	22	b	b	PROPN
ap-6836	205	23	≥	≥	NUM
ap-6836	205	24	c	c	NOUN
ap-6836	205	25	,	,	PUNCT
ap-6836	205	26	the	the	DET
ap-6836	205	27	following	follow	VERB
ap-6836	205	28	number	number	NOUN
ap-6836	205	29	is	be	AUX
ap-6836	205	30	antipalindromic	antipalindromic	ADJ
ap-6836	205	31	:	:	PUNCT
ap-6836	206	1	[	[	X
ap-6836	206	2	m	m	X
ap-6836	206	3	·	·	PUNCT
ap-6836	206	4	(	(	PUNCT
ap-6836	206	5	b−	b−	NOUN
ap-6836	206	6	1)]k	1)]k	NUM
ap-6836	206	7	.	.	PUNCT
ap-6836	207	1	it	it	PRON
ap-6836	207	2	suffices	suffice	VERB
ap-6836	207	3	to	to	PART
ap-6836	207	4	put	put	VERB
ap-6836	207	5	c	c	NOUN
ap-6836	207	6	=	=	SYM
ap-6836	207	7	(	(	PUNCT
ap-6836	207	8	k	k	PROPN
ap-6836	207	9	k−1	k−1	PROPN
ap-6836	207	10	2	2	NUM
ap-6836	207	11	)	)	PUNCT
ap-6836	207	12	·	·	PUNCT
ap-6836	207	13	mk	mk	X
ap-6836	207	14	.	.	PUNCT
ap-6836	208	1	proof	proof	NOUN
ap-6836	208	2	.	.	PUNCT
ap-6836	209	1	the	the	DET
ap-6836	209	2	binomial	binomial	ADJ
ap-6836	209	3	theorem	theorem	NOUN
ap-6836	209	4	reads	read	NOUN
ap-6836	209	5	[	[	X
ap-6836	209	6	m	m	X
ap-6836	209	7	·	·	PUNCT
ap-6836	209	8	(	(	PUNCT
ap-6836	209	9	b−	b−	NOUN
ap-6836	209	10	1)]k	1)]k	NUM
ap-6836	209	11	=	=	SYM
ap-6836	209	12	mk	mk	PROPN
ap-6836	209	13	·	·	PUNCT
ap-6836	209	14	k∑	k∑	PROPN
ap-6836	210	1	i=0	i=0	PROPN
ap-6836	210	2	(	(	PUNCT
ap-6836	210	3	−1)i	−1)i	X
ap-6836	210	4	·	·	PUNCT
ap-6836	210	5	(	(	PUNCT
ap-6836	210	6	k	k	X
ap-6836	210	7	i	i	PROPN
ap-6836	210	8	)	)	PUNCT
ap-6836	210	9	·	·	PUNCT
ap-6836	210	10	bk−i	bk−i	NOUN
ap-6836	210	11	.	.	PUNCT
ap-6836	211	1	since	since	SCONJ
ap-6836	211	2	(	(	PUNCT
ap-6836	211	3	k	k	PROPN
ap-6836	211	4	k−1	k−1	PROPN
ap-6836	211	5	2	2	NUM
ap-6836	211	6	)	)	PUNCT
ap-6836	211	7	is	be	AUX
ap-6836	211	8	the	the	DET
ap-6836	211	9	maximum	maximum	ADJ
ap-6836	211	10	number	number	NOUN
ap-6836	211	11	among	among	ADP
ap-6836	211	12	(	(	PUNCT
ap-6836	211	13	k	k	X
ap-6836	211	14	i	i	PROPN
ap-6836	211	15	)	)	PUNCT
ap-6836	211	16	for	for	ADP
ap-6836	211	17	i	i	PROPN
ap-6836	211	18	∈	∈	PROPN
ap-6836	211	19	{	{	PUNCT
ap-6836	211	20	0	0	NUM
ap-6836	211	21	,	,	PUNCT
ap-6836	211	22	1	1	NUM
ap-6836	211	23	,	,	PUNCT
ap-6836	211	24	.	.	PUNCT
ap-6836	211	25	.	.	PUNCT
ap-6836	212	1	.	.	PUNCT
ap-6836	213	1	,	,	PUNCT
ap-6836	213	2	k	k	X
ap-6836	213	3	}	}	PUNCT
ap-6836	213	4	,	,	PUNCT
ap-6836	213	5	the	the	DET
ap-6836	213	6	expansion	expansion	NOUN
ap-6836	213	7	in	in	ADP
ap-6836	213	8	base	base	PROPN
ap-6836	213	9	b	b	PROPN
ap-6836	213	10	equals	equal	VERB
ap-6836	213	11	:(	:(	PUNCT
ap-6836	214	1	[	[	X
ap-6836	214	2	m	m	X
ap-6836	214	3	·	·	PUNCT
ap-6836	214	4	(	(	PUNCT
ap-6836	214	5	b−	b−	NOUN
ap-6836	214	6	1)]k	1)]k	NUM
ap-6836	214	7	)	)	PUNCT
ap-6836	215	1	b	b	X
ap-6836	215	2	=	=	SYM
ap-6836	215	3	=	=	SYM
ap-6836	215	4	(	(	PUNCT
ap-6836	215	5	mk	mk	X
ap-6836	215	6	·	·	PUNCT
ap-6836	215	7	(	(	PUNCT
ap-6836	215	8	k	k	NOUN
ap-6836	215	9	0	0	NUM
ap-6836	215	10	)	)	PUNCT
ap-6836	216	1	−	−	PROPN
ap-6836	216	2	1	1	NUM
ap-6836	216	3	)	)	PUNCT
ap-6836	216	4	(	(	PUNCT
ap-6836	216	5	b−mk	b−mk	PROPN
ap-6836	216	6	·	·	PUNCT
ap-6836	216	7	(	(	PUNCT
ap-6836	216	8	k	k	NOUN
ap-6836	216	9	1	1	NUM
ap-6836	216	10	)	)	PUNCT
ap-6836	216	11	)	)	PUNCT
ap-6836	216	12	(	(	PUNCT
ap-6836	216	13	mk	mk	X
ap-6836	216	14	·	·	PUNCT
ap-6836	216	15	(	(	PUNCT
ap-6836	216	16	k	k	NOUN
ap-6836	216	17	2	2	X
ap-6836	216	18	)	)	PUNCT
ap-6836	216	19	−	−	PROPN
ap-6836	216	20	1	1	NUM
ap-6836	216	21	)	)	PUNCT
ap-6836	216	22	.	.	PUNCT
ap-6836	216	23	.	.	PUNCT
ap-6836	216	24	.	.	PUNCT
ap-6836	216	25	.	.	PUNCT
ap-6836	216	26	.	.	PUNCT
ap-6836	216	27	.	.	PUNCT
ap-6836	217	1	(	(	PUNCT
ap-6836	217	2	b−mk	b−mk	PROPN
ap-6836	217	3	·	·	PUNCT
ap-6836	217	4	(	(	PUNCT
ap-6836	217	5	k	k	PROPN
ap-6836	217	6	k−2	k−2	PROPN
ap-6836	217	7	)	)	PUNCT
ap-6836	217	8	)	)	PUNCT
ap-6836	217	9	(	(	PUNCT
ap-6836	217	10	mk	mk	X
ap-6836	217	11	·	·	PUNCT
ap-6836	217	12	(	(	PUNCT
ap-6836	217	13	k	k	PROPN
ap-6836	217	14	k−1	k−1	PROPN
ap-6836	217	15	)	)	PUNCT
ap-6836	217	16	−	−	PROPN
ap-6836	218	1	1	1	NUM
ap-6836	218	2	)	)	PUNCT
ap-6836	218	3	(	(	PUNCT
ap-6836	218	4	b−mk	b−mk	PROPN
ap-6836	218	5	·	·	PUNCT
ap-6836	218	6	(	(	PUNCT
ap-6836	218	7	k	k	X
ap-6836	218	8	k	k	PROPN
ap-6836	218	9	)	)	PUNCT
ap-6836	218	10	)	)	PUNCT
ap-6836	218	11	.	.	PUNCT
ap-6836	219	1	5	5	X
ap-6836	219	2	.	.	X
ap-6836	219	3	multi	multi	ADJ
ap-6836	219	4	-	-	ADJ
ap-6836	219	5	base	base	ADJ
ap-6836	219	6	antipalindromic	antipalindromic	ADJ
ap-6836	219	7	numbers	number	NOUN
ap-6836	219	8	let	let	VERB
ap-6836	219	9	us	we	PRON
ap-6836	219	10	study	study	VERB
ap-6836	219	11	the	the	DET
ap-6836	219	12	question	question	NOUN
ap-6836	219	13	whether	whether	SCONJ
ap-6836	219	14	there	there	PRON
ap-6836	219	15	are	be	VERB
ap-6836	219	16	numbers	number	NOUN
ap-6836	219	17	that	that	PRON
ap-6836	219	18	are	be	AUX
ap-6836	219	19	antipalindromic	antipalindromic	ADJ
ap-6836	219	20	simultaneously	simultaneously	ADV
ap-6836	219	21	in	in	ADP
ap-6836	219	22	more	more	ADJ
ap-6836	219	23	bases	basis	NOUN
ap-6836	219	24	.	.	PUNCT
ap-6836	220	1	bašić	bašić	ADV
ap-6836	220	2	in	in	ADP
ap-6836	220	3	[	[	X
ap-6836	220	4	11	11	NUM
ap-6836	220	5	,	,	PUNCT
ap-6836	220	6	12	12	NUM
ap-6836	220	7	]	]	PUNCT
ap-6836	220	8	showed	show	VERB
ap-6836	220	9	that	that	SCONJ
ap-6836	220	10	for	for	ADP
ap-6836	220	11	any	any	DET
ap-6836	220	12	n	n	PRON
ap-6836	220	13	∈	∈	NOUN
ap-6836	220	14	n	n	NOUN
ap-6836	220	15	and	and	CCONJ
ap-6836	220	16	any	any	DET
ap-6836	220	17	d	d	NOUN
ap-6836	220	18	≥	≥	NUM
ap-6836	220	19	2	2	NUM
ap-6836	220	20	,	,	PUNCT
ap-6836	220	21	there	there	PRON
ap-6836	220	22	exists	exist	VERB
ap-6836	220	23	an	an	DET
ap-6836	220	24	integer	integer	NOUN
ap-6836	220	25	m	m	NOUN
ap-6836	220	26	and	and	CCONJ
ap-6836	220	27	a	a	DET
ap-6836	220	28	list	list	NOUN
ap-6836	220	29	of	of	ADP
ap-6836	220	30	n	n	NOUN
ap-6836	220	31	bases	basis	NOUN
ap-6836	220	32	such	such	ADJ
ap-6836	220	33	that	that	SCONJ
ap-6836	220	34	m	m	PROPN
ap-6836	220	35	is	be	AUX
ap-6836	220	36	a	a	DET
ap-6836	220	37	d	d	ADJ
ap-6836	220	38	-	-	PUNCT
ap-6836	220	39	digit	digit	NOUN
ap-6836	220	40	palindromic	palindromic	ADJ
ap-6836	220	41	number	number	NOUN
ap-6836	220	42	in	in	ADP
ap-6836	220	43	each	each	PRON
ap-6836	220	44	of	of	ADP
ap-6836	220	45	the	the	DET
ap-6836	220	46	bases	basis	NOUN
ap-6836	220	47	.	.	PUNCT
ap-6836	221	1	we	we	PRON
ap-6836	221	2	do	do	AUX
ap-6836	221	3	not	not	PART
ap-6836	221	4	know	know	VERB
ap-6836	221	5	whether	whether	SCONJ
ap-6836	221	6	something	something	PRON
ap-6836	221	7	similar	similar	ADJ
ap-6836	221	8	holds	hold	VERB
ap-6836	221	9	for	for	ADP
ap-6836	221	10	antipalindromic	antipalindromic	ADJ
ap-6836	221	11	numbers	number	NOUN
ap-6836	221	12	.	.	PUNCT
ap-6836	222	1	we	we	PRON
ap-6836	222	2	will	will	AUX
ap-6836	222	3	show	show	VERB
ap-6836	222	4	a	a	DET
ap-6836	222	5	weaker	weak	ADJ
ap-6836	222	6	statement	statement	NOUN
ap-6836	222	7	that	that	SCONJ
ap-6836	222	8	for	for	ADP
ap-6836	222	9	any	any	DET
ap-6836	222	10	n	n	PRON
ap-6836	222	11	∈	∈	PROPN
ap-6836	222	12	n	n	CCONJ
ap-6836	222	13	,	,	PUNCT
ap-6836	222	14	there	there	PRON
ap-6836	222	15	exists	exist	VERB
ap-6836	222	16	an	an	DET
ap-6836	222	17	integer	integer	NOUN
ap-6836	222	18	m	m	NOUN
ap-6836	222	19	and	and	CCONJ
ap-6836	222	20	a	a	DET
ap-6836	222	21	list	list	NOUN
ap-6836	222	22	of	of	ADP
ap-6836	222	23	n	n	NOUN
ap-6836	222	24	bases	basis	NOUN
ap-6836	222	25	such	such	ADJ
ap-6836	222	26	that	that	SCONJ
ap-6836	222	27	m	m	PROPN
ap-6836	222	28	is	be	AUX
ap-6836	222	29	antipalindromic	antipalindromic	ADJ
ap-6836	222	30	in	in	ADP
ap-6836	222	31	each	each	PRON
ap-6836	222	32	of	of	ADP
ap-6836	222	33	the	the	DET
ap-6836	222	34	bases	basis	NOUN
ap-6836	222	35	.	.	PUNCT
ap-6836	223	1	431	431	NUM
ap-6836	223	2	ľ	ľ	X
ap-6836	223	3	.	.	PUNCT
ap-6836	224	1	dvořáková	dvořáková	PROPN
ap-6836	224	2	,	,	PUNCT
ap-6836	224	3	s.	s.	PROPN
ap-6836	224	4	kruml	kruml	PROPN
ap-6836	224	5	,	,	PUNCT
ap-6836	224	6	d.	d.	PROPN
ap-6836	224	7	ryzák	ryzák	VERB
ap-6836	224	8	acta	acta	PROPN
ap-6836	224	9	polytechnica	polytechnica	PROPN
ap-6836	224	10	base	base	PROPN
ap-6836	224	11	expansion	expansion	NOUN
ap-6836	224	12	2	2	NUM
ap-6836	224	13	110011001100	110011001100	NUM
ap-6836	224	14	4	4	NUM
ap-6836	224	15	303030	303030	NUM
ap-6836	224	16	10	10	NUM
ap-6836	224	17	3276	3276	NUM
ap-6836	224	18	64	64	NUM
ap-6836	224	19	(	(	PUNCT
ap-6836	224	20	53)(10	53)(10	NOUN
ap-6836	224	21	)	)	PUNCT
ap-6836	224	22	79	79	NUM
ap-6836	224	23	(	(	PUNCT
ap-6836	224	24	41)(37	41)(37	NUM
ap-6836	224	25	)	)	SYM
ap-6836	224	26	85	85	NUM
ap-6836	224	27	(	(	PUNCT
ap-6836	224	28	38)(46	38)(46	NUM
ap-6836	224	29	)	)	PUNCT
ap-6836	224	30	92	92	NUM
ap-6836	224	31	(	(	PUNCT
ap-6836	224	32	35)(56	35)(56	NUM
ap-6836	224	33	)	)	PUNCT
ap-6836	224	34	118	118	NUM
ap-6836	224	35	(	(	PUNCT
ap-6836	224	36	27)(90	27)(90	NUM
ap-6836	224	37	)	)	PUNCT
ap-6836	224	38	127	127	NUM
ap-6836	224	39	(	(	PUNCT
ap-6836	224	40	25)(101	25)(101	NUM
ap-6836	224	41	)	)	PUNCT
ap-6836	224	42	157	157	NUM
ap-6836	224	43	(	(	PUNCT
ap-6836	224	44	20)(136	20)(136	NUM
ap-6836	224	45	)	)	PUNCT
ap-6836	224	46	183	183	NUM
ap-6836	224	47	(	(	PUNCT
ap-6836	224	48	17)(165	17)(165	NUM
ap-6836	224	49	)	)	SYM
ap-6836	224	50	235	235	NUM
ap-6836	224	51	(	(	PUNCT
ap-6836	224	52	13)(221	13)(221	NUM
ap-6836	224	53	)	)	PUNCT
ap-6836	224	54	253	253	NUM
ap-6836	224	55	(	(	PUNCT
ap-6836	224	56	12)(240	12)(240	NUM
ap-6836	224	57	)	)	PUNCT
ap-6836	224	58	274	274	NUM
ap-6836	224	59	(	(	PUNCT
ap-6836	224	60	11)(262	11)(262	NUM
ap-6836	224	61	)	)	PUNCT
ap-6836	224	62	365	365	NUM
ap-6836	224	63	(	(	PUNCT
ap-6836	224	64	8)(356	8)(356	NOUN
ap-6836	224	65	)	)	PUNCT
ap-6836	224	66	469	469	NUM
ap-6836	224	67	(	(	PUNCT
ap-6836	224	68	6)(462	6)(462	NOUN
ap-6836	224	69	)	)	PUNCT
ap-6836	224	70	547	547	NUM
ap-6836	224	71	(	(	PUNCT
ap-6836	224	72	5)(541	5)(541	NUM
ap-6836	224	73	)	)	PUNCT
ap-6836	224	74	820	820	NUM
ap-6836	224	75	(	(	PUNCT
ap-6836	224	76	3)(816	3)(816	NUM
ap-6836	224	77	)	)	PUNCT
ap-6836	224	78	1093	1093	NUM
ap-6836	224	79	(	(	PUNCT
ap-6836	224	80	2)(1090	2)(1090	NUM
ap-6836	224	81	)	)	PUNCT
ap-6836	224	82	1639	1639	NUM
ap-6836	224	83	(	(	PUNCT
ap-6836	224	84	1)(1637	1)(1637	NUM
ap-6836	224	85	)	)	PUNCT
ap-6836	224	86	6553	6553	NUM
ap-6836	224	87	(	(	PUNCT
ap-6836	224	88	3276	3276	NUM
ap-6836	224	89	)	)	PUNCT
ap-6836	224	90	table	table	NOUN
ap-6836	224	91	3	3	NUM
ap-6836	224	92	.	.	PUNCT
ap-6836	225	1	antipalindromic	antipalindromic	ADJ
ap-6836	225	2	expansions	expansion	NOUN
ap-6836	225	3	of	of	ADP
ap-6836	225	4	the	the	DET
ap-6836	225	5	number	number	NOUN
ap-6836	225	6	3276	3276	NUM
ap-6836	225	7	in	in	ADP
ap-6836	225	8	21	21	NUM
ap-6836	225	9	bases	basis	NOUN
ap-6836	225	10	in	in	ADP
ap-6836	225	11	2014	2014	NUM
ap-6836	225	12	,	,	PUNCT
ap-6836	225	13	bérczes	bércze	NOUN
ap-6836	225	14	and	and	CCONJ
ap-6836	225	15	ziegler	ziegler	NOUN
ap-6836	226	1	[	[	X
ap-6836	226	2	13	13	NUM
ap-6836	226	3	]	]	PUNCT
ap-6836	226	4	discussed	discuss	VERB
ap-6836	226	5	multibase	multibase	ADJ
ap-6836	226	6	palindromic	palindromic	ADJ
ap-6836	226	7	numbers	number	NOUN
ap-6836	226	8	and	and	CCONJ
ap-6836	226	9	proposed	propose	VERB
ap-6836	226	10	a	a	DET
ap-6836	226	11	list	list	NOUN
ap-6836	226	12	of	of	ADP
ap-6836	226	13	the	the	DET
ap-6836	226	14	first	first	ADJ
ap-6836	226	15	53	53	NUM
ap-6836	226	16	numbers	number	NOUN
ap-6836	226	17	palindromic	palindromic	ADJ
ap-6836	226	18	in	in	ADP
ap-6836	226	19	bases	basis	NOUN
ap-6836	226	20	2	2	NUM
ap-6836	226	21	and	and	CCONJ
ap-6836	226	22	10	10	NUM
ap-6836	226	23	simultaneously	simultaneously	ADV
ap-6836	226	24	.	.	PUNCT
ap-6836	227	1	our	our	PRON
ap-6836	227	2	application	application	NOUN
ap-6836	227	3	[	[	X
ap-6836	227	4	9	9	NUM
ap-6836	227	5	]	]	PUNCT
ap-6836	227	6	has	have	AUX
ap-6836	227	7	only	only	ADV
ap-6836	227	8	been	be	AUX
ap-6836	227	9	able	able	ADJ
ap-6836	227	10	to	to	PART
ap-6836	227	11	find	find	VERB
ap-6836	227	12	one	one	NUM
ap-6836	227	13	number	number	NOUN
ap-6836	227	14	with	with	ADP
ap-6836	227	15	an	an	DET
ap-6836	227	16	antipalindromic	antipalindromic	ADJ
ap-6836	227	17	expansion	expansion	NOUN
ap-6836	227	18	in	in	ADP
ap-6836	227	19	these	these	DET
ap-6836	227	20	bases	basis	NOUN
ap-6836	227	21	.	.	PUNCT
ap-6836	228	1	this	this	DET
ap-6836	228	2	number	number	NOUN
ap-6836	228	3	,	,	PUNCT
ap-6836	228	4	3276	3276	NUM
ap-6836	228	5	,	,	PUNCT
ap-6836	228	6	is	be	AUX
ap-6836	228	7	also	also	ADV
ap-6836	228	8	antipalindromic	antipalindromic	ADJ
ap-6836	228	9	in	in	ADP
ap-6836	228	10	other	other	ADJ
ap-6836	228	11	19	19	NUM
ap-6836	228	12	distinct	distinct	ADJ
ap-6836	228	13	bases	basis	NOUN
ap-6836	228	14	,	,	PUNCT
ap-6836	228	15	see	see	VERB
ap-6836	228	16	table	table	NOUN
ap-6836	228	17	3	3	NUM
ap-6836	228	18	.	.	PUNCT
ap-6836	229	1	the	the	DET
ap-6836	229	2	next	next	ADJ
ap-6836	229	3	greater	great	ADJ
ap-6836	229	4	number	number	NOUN
ap-6836	229	5	that	that	PRON
ap-6836	229	6	is	be	AUX
ap-6836	229	7	antipalindromic	antipalindromic	ADJ
ap-6836	229	8	both	both	CCONJ
ap-6836	229	9	in	in	ADP
ap-6836	229	10	base	base	NOUN
ap-6836	229	11	2	2	NUM
ap-6836	229	12	and	and	CCONJ
ap-6836	229	13	10	10	NUM
ap-6836	229	14	must	must	AUX
ap-6836	229	15	be	be	AUX
ap-6836	229	16	greater	great	ADJ
ap-6836	229	17	than	than	ADP
ap-6836	229	18	1010	1010	NUM
ap-6836	229	19	and	and	CCONJ
ap-6836	229	20	divisible	divisible	ADJ
ap-6836	229	21	by	by	ADP
ap-6836	229	22	18	18	NUM
ap-6836	229	23	.	.	PUNCT
ap-6836	230	1	it	it	PRON
ap-6836	230	2	is	be	AUX
ap-6836	230	3	not	not	PART
ap-6836	230	4	uncommon	uncommon	ADJ
ap-6836	230	5	for	for	SCONJ
ap-6836	230	6	a	a	DET
ap-6836	230	7	number	number	NOUN
ap-6836	230	8	to	to	PART
ap-6836	230	9	be	be	AUX
ap-6836	230	10	antipalindromic	antipalindromic	ADJ
ap-6836	230	11	in	in	ADP
ap-6836	230	12	more	more	ADJ
ap-6836	230	13	bases	basis	NOUN
ap-6836	230	14	.	.	PUNCT
ap-6836	231	1	in	in	ADP
ap-6836	231	2	this	this	DET
ap-6836	231	3	section	section	NOUN
ap-6836	231	4	,	,	PUNCT
ap-6836	231	5	we	we	PRON
ap-6836	231	6	show	show	VERB
ap-6836	231	7	that	that	SCONJ
ap-6836	231	8	if	if	SCONJ
ap-6836	231	9	a	a	DET
ap-6836	231	10	number	number	NOUN
ap-6836	231	11	is	be	AUX
ap-6836	231	12	antipalindromic	antipalindromic	ADJ
ap-6836	231	13	in	in	ADP
ap-6836	231	14	a	a	DET
ap-6836	231	15	unique	unique	ADJ
ap-6836	231	16	base	base	NOUN
ap-6836	231	17	,	,	PUNCT
ap-6836	231	18	then	then	ADV
ap-6836	231	19	the	the	DET
ap-6836	231	20	number	number	NOUN
ap-6836	231	21	must	must	AUX
ap-6836	231	22	be	be	AUX
ap-6836	231	23	prime	prime	ADJ
ap-6836	231	24	or	or	CCONJ
ap-6836	231	25	equal	equal	ADJ
ap-6836	231	26	to	to	ADP
ap-6836	231	27	1	1	NUM
ap-6836	231	28	,	,	PUNCT
ap-6836	231	29	see	see	VERB
ap-6836	231	30	theorem	theorem	VERB
ap-6836	231	31	11	11	NUM
ap-6836	231	32	.	.	PUNCT
ap-6836	232	1	definition	definition	NOUN
ap-6836	232	2	2	2	NUM
ap-6836	232	3	.	.	PUNCT
ap-6836	233	1	an	an	DET
ap-6836	233	2	antipalindromic	antipalindromic	ADJ
ap-6836	233	3	number	number	NOUN
ap-6836	233	4	is	be	AUX
ap-6836	233	5	called	call	VERB
ap-6836	233	6	multi	multi	ADJ
ap-6836	233	7	-	-	NOUN
ap-6836	233	8	base	base	NOUN
ap-6836	233	9	if	if	SCONJ
ap-6836	233	10	it	it	PRON
ap-6836	233	11	is	be	AUX
ap-6836	233	12	antipalindromic	antipalindromic	ADJ
ap-6836	233	13	in	in	ADP
ap-6836	233	14	at	at	ADV
ap-6836	233	15	least	least	ADV
ap-6836	233	16	two	two	NUM
ap-6836	233	17	different	different	ADJ
ap-6836	233	18	bases	basis	NOUN
ap-6836	233	19	.	.	PUNCT
ap-6836	234	1	observation	observation	NOUN
ap-6836	234	2	3	3	NUM
ap-6836	234	3	.	.	PUNCT
ap-6836	235	1	every	every	DET
ap-6836	235	2	number	number	NOUN
ap-6836	235	3	m	m	NOUN
ap-6836	235	4	∈	∈	NOUN
ap-6836	235	5	n	n	PRON
ap-6836	235	6	is	be	AUX
ap-6836	235	7	antipalindromic	antipalindromic	ADJ
ap-6836	235	8	in	in	ADP
ap-6836	235	9	base	base	NOUN
ap-6836	235	10	2	2	NUM
ap-6836	235	11	m	m	NOUN
ap-6836	235	12	+	+	NOUN
ap-6836	235	13	1	1	NUM
ap-6836	235	14	.	.	NOUN
ap-6836	235	15	example	example	NOUN
ap-6836	235	16	4	4	NUM
ap-6836	235	17	.	.	PUNCT
ap-6836	236	1	the	the	DET
ap-6836	236	2	number	number	NOUN
ap-6836	236	3	3276	3276	NUM
ap-6836	236	4	is	be	AUX
ap-6836	236	5	a	a	DET
ap-6836	236	6	multi	multi	ADJ
ap-6836	236	7	-	-	ADJ
ap-6836	236	8	base	base	ADJ
ap-6836	236	9	antipalindromic	antipalindromic	ADJ
ap-6836	236	10	number	number	NOUN
ap-6836	236	11	,	,	PUNCT
ap-6836	236	12	as	as	SCONJ
ap-6836	236	13	illustrated	illustrate	VERB
ap-6836	236	14	in	in	ADP
ap-6836	236	15	table	table	NOUN
ap-6836	236	16	3	3	NUM
ap-6836	236	17	.	.	PUNCT
ap-6836	236	18	theorem	theorem	VERB
ap-6836	236	19	11	11	NUM
ap-6836	236	20	.	.	PUNCT
ap-6836	237	1	for	for	ADP
ap-6836	237	2	any	any	DET
ap-6836	237	3	composite	composite	ADJ
ap-6836	237	4	number	number	NOUN
ap-6836	237	5	a	a	DET
ap-6836	237	6	∈	∈	PROPN
ap-6836	237	7	n	n	CCONJ
ap-6836	237	8	,	,	PUNCT
ap-6836	237	9	we	we	PRON
ap-6836	237	10	can	can	AUX
ap-6836	237	11	find	find	VERB
ap-6836	237	12	at	at	ADV
ap-6836	237	13	least	least	ADV
ap-6836	237	14	two	two	NUM
ap-6836	237	15	bases	basis	NOUN
ap-6836	237	16	b	b	NOUN
ap-6836	237	17	,	,	PUNCT
ap-6836	237	18	c	c	X
ap-6836	237	19	such	such	ADJ
ap-6836	237	20	that	that	SCONJ
ap-6836	237	21	this	this	DET
ap-6836	237	22	number	number	NOUN
ap-6836	237	23	has	have	VERB
ap-6836	237	24	an	an	DET
ap-6836	237	25	antipalindromic	antipalindromic	ADJ
ap-6836	237	26	expansion	expansion	NOUN
ap-6836	237	27	in	in	ADP
ap-6836	237	28	both	both	PRON
ap-6836	237	29	of	of	ADP
ap-6836	237	30	them	they	PRON
ap-6836	237	31	.	.	PUNCT
ap-6836	238	1	proof	proof	NOUN
ap-6836	238	2	.	.	PUNCT
ap-6836	239	1	assume	assume	VERB
ap-6836	239	2	that	that	SCONJ
ap-6836	239	3	a	a	DET
ap-6836	239	4	=	=	X
ap-6836	239	5	m	m	PROPN
ap-6836	239	6	·	·	PUNCT
ap-6836	239	7	n	n	CCONJ
ap-6836	239	8	,	,	PUNCT
ap-6836	239	9	m	m	PROPN
ap-6836	239	10	,	,	PUNCT
ap-6836	239	11	n	n	PROPN
ap-6836	239	12	∈	∈	PROPN
ap-6836	239	13	n	n	CCONJ
ap-6836	239	14	,	,	PUNCT
ap-6836	239	15	m	m	VERB
ap-6836	239	16	≥	≥	NOUN
ap-6836	239	17	n	n	PRON
ap-6836	239	18	≥	≥	NUM
ap-6836	239	19	2	2	NUM
ap-6836	239	20	,	,	PUNCT
ap-6836	239	21	set	set	VERB
ap-6836	239	22	b	b	NOUN
ap-6836	239	23	=	=	PUNCT
ap-6836	239	24	a	a	DET
ap-6836	239	25	n	n	NOUN
ap-6836	239	26	+	+	NUM
ap-6836	239	27	1	1	NUM
ap-6836	239	28	,	,	PUNCT
ap-6836	239	29	c	c	NOUN
ap-6836	239	30	=	=	SYM
ap-6836	239	31	2a	2a	NUM
ap-6836	240	1	+	+	CCONJ
ap-6836	240	2	1	1	X
ap-6836	240	3	.	.	PUNCT
ap-6836	240	4	the	the	DET
ap-6836	240	5	expansions	expansion	NOUN
ap-6836	240	6	of	of	ADP
ap-6836	240	7	a	a	PRON
ap-6836	240	8	in	in	ADP
ap-6836	240	9	bases	basis	NOUN
ap-6836	240	10	b	b	NOUN
ap-6836	240	11	,	,	PUNCT
ap-6836	240	12	c	c	PROPN
ap-6836	240	13	are	be	AUX
ap-6836	240	14	equal	equal	ADJ
ap-6836	240	15	to	to	ADP
ap-6836	240	16	:	:	PUNCT
ap-6836	240	17	(	(	PUNCT
ap-6836	240	18	a)b	a)b	X
ap-6836	240	19	=	=	SYM
ap-6836	240	20	(	(	PUNCT
ap-6836	240	21	n−	n−	NOUN
ap-6836	240	22	1	1	NUM
ap-6836	240	23	)	)	PUNCT
ap-6836	240	24	(	(	PUNCT
ap-6836	240	25	a	a	DET
ap-6836	240	26	n	n	NOUN
ap-6836	240	27	−	−	PROPN
ap-6836	240	28	n	n	NOUN
ap-6836	240	29	+	+	NOUN
ap-6836	240	30	1	1	NUM
ap-6836	240	31	)	)	PUNCT
ap-6836	240	32	,	,	PUNCT
ap-6836	240	33	(	(	PUNCT
ap-6836	240	34	a)c	a)c	X
ap-6836	240	35	=	=	SYM
ap-6836	240	36	a.	a.	NOUN
ap-6836	240	37	theorem	theorem	NOUN
ap-6836	240	38	12	12	NUM
ap-6836	240	39	.	.	PUNCT
ap-6836	241	1	for	for	ADP
ap-6836	241	2	every	every	DET
ap-6836	241	3	n	n	PRON
ap-6836	241	4	∈	∈	PROPN
ap-6836	241	5	n	n	CCONJ
ap-6836	241	6	,	,	PUNCT
ap-6836	241	7	there	there	PRON
ap-6836	241	8	exist	exist	VERB
ap-6836	241	9	infinitely	infinitely	ADV
ap-6836	241	10	many	many	ADJ
ap-6836	241	11	numbers	number	NOUN
ap-6836	241	12	that	that	PRON
ap-6836	241	13	are	be	AUX
ap-6836	241	14	antipalindromic	antipalindromic	ADJ
ap-6836	241	15	in	in	ADP
ap-6836	241	16	at	at	ADV
ap-6836	241	17	least	least	ADJ
ap-6836	241	18	n	n	PRON
ap-6836	241	19	bases	basis	NOUN
ap-6836	241	20	.	.	PUNCT
ap-6836	242	1	proof	proof	NOUN
ap-6836	242	2	.	.	PUNCT
ap-6836	243	1	consider	consider	VERB
ap-6836	243	2	a	a	DET
ap-6836	243	3	number	number	NOUN
ap-6836	243	4	a	a	DET
ap-6836	243	5	such	such	ADJ
ap-6836	243	6	that	that	SCONJ
ap-6836	243	7	a	a	DET
ap-6836	243	8	=	=	X
ap-6836	243	9	(	(	PUNCT
ap-6836	243	10	2n	2n	NUM
ap-6836	243	11	)	)	PUNCT
ap-6836	243	12	!	!	PUNCT
ap-6836	243	13	.	.	PUNCT
ap-6836	244	1	theorem	theorem	ADJ
ap-6836	244	2	11	11	NUM
ap-6836	244	3	indicates	indicate	VERB
ap-6836	244	4	that	that	SCONJ
ap-6836	244	5	the	the	DET
ap-6836	244	6	number	number	NOUN
ap-6836	244	7	a	a	PRON
ap-6836	244	8	is	be	AUX
ap-6836	244	9	antipalindromic	antipalindromic	ADJ
ap-6836	244	10	in	in	ADP
ap-6836	244	11	bases	basis	NOUN
ap-6836	244	12	a	a	DET
ap-6836	244	13	2	2	NUM
ap-6836	244	14	+	+	SYM
ap-6836	244	15	1	1	NUM
ap-6836	244	16	,	,	PUNCT
ap-6836	244	17	a	a	DET
ap-6836	244	18	3	3	NUM
ap-6836	244	19	+	+	SYM
ap-6836	244	20	1	1	NUM
ap-6836	244	21	,	,	PUNCT
ap-6836	244	22	.	.	PUNCT
ap-6836	244	23	.	.	PUNCT
ap-6836	245	1	.	.	PUNCT
ap-6836	246	1	,	,	PUNCT
ap-6836	246	2	a	a	DET
ap-6836	246	3	n	n	NOUN
ap-6836	246	4	+	+	CCONJ
ap-6836	246	5	1	1	NUM
ap-6836	246	6	and	and	CCONJ
ap-6836	246	7	also	also	ADV
ap-6836	246	8	2a	2a	NUM
ap-6836	246	9	+	+	CCONJ
ap-6836	246	10	1	1	X
ap-6836	246	11	.	.	X
ap-6836	246	12	theorem	theorem	VERB
ap-6836	246	13	13	13	NUM
ap-6836	246	14	.	.	PUNCT
ap-6836	247	1	let	let	VERB
ap-6836	247	2	b	b	PROPN
ap-6836	247	3	∈	∈	PROPN
ap-6836	247	4	n	n	CCONJ
ap-6836	247	5	,	,	PUNCT
ap-6836	247	6	b	b	PROPN
ap-6836	247	7	≥	≥	NUM
ap-6836	247	8	2	2	NUM
ap-6836	247	9	.	.	PUNCT
ap-6836	248	1	then	then	ADV
ap-6836	248	2	there	there	PRON
ap-6836	248	3	exists	exist	VERB
ap-6836	248	4	m	m	VERB
ap-6836	248	5	∈	∈	PROPN
ap-6836	248	6	n	n	PRON
ap-6836	248	7	such	such	ADJ
ap-6836	248	8	that	that	SCONJ
ap-6836	248	9	m	m	PROPN
ap-6836	248	10	is	be	AUX
ap-6836	248	11	antipalindromic	antipalindromic	ADJ
ap-6836	248	12	in	in	ADP
ap-6836	248	13	base	base	PROPN
ap-6836	248	14	b	b	PROPN
ap-6836	248	15	and	and	CCONJ
ap-6836	248	16	in	in	ADP
ap-6836	248	17	at	at	ADV
ap-6836	248	18	least	least	ADV
ap-6836	248	19	one	one	NUM
ap-6836	248	20	more	more	ADJ
ap-6836	248	21	base	base	NOUN
ap-6836	248	22	less	less	ADJ
ap-6836	248	23	than	than	ADP
ap-6836	248	24	m.	m.	NOUN
ap-6836	248	25	proof	proof	NOUN
ap-6836	248	26	.	.	PUNCT
ap-6836	249	1	base	base	PROPN
ap-6836	249	2	b	b	PROPN
ap-6836	249	3	m	m	VERB
ap-6836	249	4	two	two	NUM
ap-6836	249	5	expansions	expansion	NOUN
ap-6836	249	6	2	2	NUM
ap-6836	249	7	12	12	NUM
ap-6836	249	8	(	(	PUNCT
ap-6836	249	9	12)2	12)2	NUM
ap-6836	249	10	=	=	SYM
ap-6836	249	11	1100	1100	NUM
ap-6836	249	12	(	(	PUNCT
ap-6836	249	13	12)4	12)4	NUM
ap-6836	249	14	=	=	SYM
ap-6836	249	15	30	30	NUM
ap-6836	249	16	3	3	NUM
ap-6836	249	17	72	72	NUM
ap-6836	249	18	(	(	PUNCT
ap-6836	249	19	72)3	72)3	NUM
ap-6836	249	20	=	=	SYM
ap-6836	249	21	2200	2200	NUM
ap-6836	249	22	(	(	PUNCT
ap-6836	249	23	72)9	72)9	NUM
ap-6836	249	24	=	=	SYM
ap-6836	249	25	80	80	NUM
ap-6836	249	26	≥	≥	NOUN
ap-6836	249	27	4	4	NUM
ap-6836	249	28	4	4	NUM
ap-6836	249	29	·	·	PUNCT
ap-6836	249	30	(	(	PUNCT
ap-6836	249	31	b−	b−	NOUN
ap-6836	249	32	1	1	NUM
ap-6836	249	33	)	)	PUNCT
ap-6836	249	34	(	(	PUNCT
ap-6836	249	35	m)b	m)b	NOUN
ap-6836	249	36	=	=	PUNCT
ap-6836	249	37	(	(	PUNCT
ap-6836	249	38	3)(b−	3)(b−	NUM
ap-6836	249	39	4	4	NUM
ap-6836	249	40	)	)	PUNCT
ap-6836	249	41	(	(	PUNCT
ap-6836	249	42	m)2b−1	m)2b−1	NOUN
ap-6836	249	43	=	=	SYM
ap-6836	249	44	(	(	PUNCT
ap-6836	249	45	1)(2b−	1)(2b−	NUM
ap-6836	249	46	3	3	NUM
ap-6836	249	47	)	)	PUNCT
ap-6836	249	48	theorem	theorem	NOUN
ap-6836	249	49	14	14	NUM
ap-6836	249	50	.	.	PUNCT
ap-6836	250	1	let	let	VERB
ap-6836	250	2	p	p	PRON
ap-6836	250	3	,	,	PUNCT
ap-6836	250	4	q	q	PUNCT
ap-6836	250	5	∈	∈	PROPN
ap-6836	250	6	n	n	PRON
ap-6836	250	7	such	such	ADJ
ap-6836	251	1	that	that	SCONJ
ap-6836	251	2	gcd(p	gcd(p	PROPN
ap-6836	251	3	,	,	PUNCT
ap-6836	251	4	q	q	NOUN
ap-6836	251	5	)	)	PUNCT
ap-6836	251	6	=	=	SYM
ap-6836	251	7	d	d	PROPN
ap-6836	251	8	and	and	CCONJ
ap-6836	251	9	p	p	X
ap-6836	251	10	≥	≥	NOUN
ap-6836	251	11	q	q	PROPN
ap-6836	251	12	d	d	X
ap-6836	251	13	>	>	X
ap-6836	251	14	1	1	NUM
ap-6836	251	15	,	,	PUNCT
ap-6836	251	16	q	q	X
ap-6836	251	17	≥	≥	NOUN
ap-6836	251	18	p	p	X
ap-6836	251	19	d	d	X
ap-6836	251	20	>	>	X
ap-6836	251	21	1	1	NUM
ap-6836	251	22	.	.	PUNCT
ap-6836	252	1	then	then	ADV
ap-6836	252	2	the	the	DET
ap-6836	252	3	number	number	NOUN
ap-6836	252	4	m	m	NOUN
ap-6836	252	5	=	=	SYM
ap-6836	252	6	pq	pq	NOUN
ap-6836	252	7	d	d	NOUN
ap-6836	252	8	is	be	AUX
ap-6836	252	9	antipalindromic	antipalindromic	ADJ
ap-6836	252	10	in	in	ADP
ap-6836	252	11	bases	basis	NOUN
ap-6836	252	12	p	p	X
ap-6836	252	13	+	+	CCONJ
ap-6836	252	14	1	1	NUM
ap-6836	252	15	and	and	CCONJ
ap-6836	252	16	q	q	NOUN
ap-6836	253	1	+	+	NOUN
ap-6836	253	2	1	1	X
ap-6836	253	3	.	.	X
ap-6836	254	1	proof	proof	NOUN
ap-6836	254	2	.	.	PUNCT
ap-6836	255	1	we	we	PRON
ap-6836	255	2	have	have	VERB
ap-6836	255	3	(	(	PUNCT
ap-6836	255	4	m)p+1	m)p+1	NOUN
ap-6836	255	5	=	=	SYM
ap-6836	255	6	(	(	PUNCT
ap-6836	255	7	q	q	NOUN
ap-6836	256	1	d	d	NOUN
ap-6836	256	2	−	−	X
ap-6836	256	3	1)(p	1)(p	NUM
ap-6836	256	4	+	+	SYM
ap-6836	256	5	1−	1−	NUM
ap-6836	256	6	q	q	NOUN
ap-6836	256	7	d	d	NOUN
ap-6836	256	8	)	)	PUNCT
ap-6836	256	9	,	,	PUNCT
ap-6836	256	10	(	(	PUNCT
ap-6836	256	11	m)q+1	m)q+1	NOUN
ap-6836	256	12	=	=	PUNCT
ap-6836	256	13	(	(	PUNCT
ap-6836	256	14	p	p	X
ap-6836	256	15	d	d	X
ap-6836	256	16	−	−	PROPN
ap-6836	256	17	1)(q	1)(q	NUM
ap-6836	256	18	+	+	CCONJ
ap-6836	256	19	1−	1−	NUM
ap-6836	256	20	p	p	NOUN
ap-6836	256	21	d	d	PROPN
ap-6836	256	22	)	)	PUNCT
ap-6836	256	23	.	.	PUNCT
ap-6836	256	24	example	example	NOUN
ap-6836	256	25	5	5	NUM
ap-6836	256	26	.	.	PUNCT
ap-6836	257	1	let	let	VERB
ap-6836	257	2	p	p	NOUN
ap-6836	257	3	=	=	NOUN
ap-6836	257	4	4	4	NUM
ap-6836	257	5	,	,	PUNCT
ap-6836	257	6	q	q	NOUN
ap-6836	257	7	=	=	SYM
ap-6836	257	8	6	6	NUM
ap-6836	257	9	,	,	PUNCT
ap-6836	257	10	then	then	ADV
ap-6836	257	11	gcd(4	gcd(4	ADJ
ap-6836	257	12	,	,	PUNCT
ap-6836	257	13	6	6	NUM
ap-6836	257	14	)	)	PUNCT
ap-6836	258	1	=	=	SYM
ap-6836	258	2	2	2	X
ap-6836	258	3	.	.	PUNCT
ap-6836	259	1	the	the	DET
ap-6836	259	2	number	number	NOUN
ap-6836	259	3	m	m	NOUN
ap-6836	259	4	=	=	NOUN
ap-6836	259	5	12	12	NUM
ap-6836	259	6	is	be	AUX
ap-6836	259	7	antipalindromic	antipalindromic	ADJ
ap-6836	259	8	in	in	ADP
ap-6836	259	9	bases	basis	NOUN
ap-6836	259	10	5	5	NUM
ap-6836	259	11	and	and	CCONJ
ap-6836	259	12	7	7	NUM
ap-6836	259	13	:	:	PUNCT
ap-6836	259	14	(	(	PUNCT
ap-6836	259	15	12)5	12)5	NUM
ap-6836	259	16	=	=	SYM
ap-6836	259	17	22	22	NUM
ap-6836	259	18	,	,	PUNCT
ap-6836	259	19	(	(	PUNCT
ap-6836	259	20	12)7	12)7	NUM
ap-6836	259	21	=	=	SYM
ap-6836	259	22	15	15	NUM
ap-6836	259	23	.	.	PUNCT
ap-6836	260	1	in	in	ADP
ap-6836	260	2	the	the	DET
ap-6836	260	3	introduction	introduction	NOUN
ap-6836	260	4	part	part	NOUN
ap-6836	260	5	,	,	PUNCT
ap-6836	260	6	we	we	PRON
ap-6836	260	7	have	have	AUX
ap-6836	260	8	mentioned	mention	VERB
ap-6836	260	9	that	that	SCONJ
ap-6836	260	10	a	a	DET
ap-6836	260	11	palindromic	palindromic	ADJ
ap-6836	260	12	number	number	NOUN
ap-6836	260	13	in	in	ADP
ap-6836	260	14	base	base	PROPN
ap-6836	260	15	b	b	PROPN
ap-6836	260	16	whose	whose	DET
ap-6836	260	17	expansion	expansion	NOUN
ap-6836	260	18	is	be	AUX
ap-6836	260	19	made	make	VERB
ap-6836	260	20	up	up	ADP
ap-6836	260	21	of	of	ADP
ap-6836	260	22	palindromic	palindromic	ADJ
ap-6836	260	23	sequences	sequence	NOUN
ap-6836	260	24	of	of	ADP
ap-6836	260	25	length	length	NOUN
ap-6836	260	26	`	`	PUNCT
ap-6836	260	27	arranged	arrange	VERB
ap-6836	260	28	in	in	ADP
ap-6836	260	29	a	a	DET
ap-6836	260	30	palindromic	palindromic	ADJ
ap-6836	260	31	order	order	NOUN
ap-6836	260	32	is	be	AUX
ap-6836	260	33	palindromic	palindromic	ADJ
ap-6836	260	34	in	in	ADP
ap-6836	260	35	base	base	NOUN
ap-6836	260	36	b	b	NOUN
ap-6836	260	37	`	`	PUNCT
ap-6836	260	38	.	.	PUNCT
ap-6836	261	1	let	let	VERB
ap-6836	261	2	us	we	PRON
ap-6836	261	3	present	present	VERB
ap-6836	261	4	a	a	DET
ap-6836	261	5	similar	similar	ADJ
ap-6836	261	6	statement	statement	NOUN
ap-6836	261	7	for	for	ADP
ap-6836	261	8	antipalindromic	antipalindromic	ADJ
ap-6836	261	9	numbers	number	NOUN
ap-6836	261	10	.	.	PUNCT
ap-6836	262	1	for	for	ADP
ap-6836	262	2	its	its	PRON
ap-6836	262	3	proof	proof	NOUN
ap-6836	262	4	,	,	PUNCT
ap-6836	262	5	we	we	PRON
ap-6836	262	6	will	will	AUX
ap-6836	262	7	need	need	VERB
ap-6836	262	8	the	the	DET
ap-6836	262	9	following	follow	VERB
ap-6836	262	10	definition	definition	NOUN
ap-6836	262	11	.	.	PUNCT
ap-6836	263	1	definition	definition	NOUN
ap-6836	263	2	3	3	X
ap-6836	263	3	.	.	PUNCT
ap-6836	264	1	let	let	VERB
ap-6836	264	2	b	b	PROPN
ap-6836	264	3	∈	∈	PROPN
ap-6836	264	4	n	n	CCONJ
ap-6836	264	5	,	,	PUNCT
ap-6836	264	6	b	b	PROPN
ap-6836	264	7	≥	≥	NUM
ap-6836	264	8	2	2	NUM
ap-6836	264	9	.	.	PUNCT
ap-6836	264	10	consider	consider	VERB
ap-6836	264	11	a	a	DET
ap-6836	264	12	string	string	NOUN
ap-6836	264	13	u	u	NOUN
ap-6836	264	14	=	=	X
ap-6836	264	15	u0u1	u0u1	PROPN
ap-6836	264	16	.	.	PUNCT
ap-6836	264	17	.	.	PUNCT
ap-6836	264	18	.	.	PUNCT
ap-6836	265	1	un	un	PROPN
ap-6836	265	2	,	,	PUNCT
ap-6836	265	3	where	where	SCONJ
ap-6836	265	4	ui	ui	PROPN
ap-6836	265	5	∈	∈	PROPN
ap-6836	265	6	{	{	PUNCT
ap-6836	265	7	0	0	NUM
ap-6836	265	8	,	,	PUNCT
ap-6836	265	9	1	1	NUM
ap-6836	265	10	,	,	PUNCT
ap-6836	265	11	.	.	PUNCT
ap-6836	265	12	.	.	PUNCT
ap-6836	265	13	.	.	PUNCT
ap-6836	266	1	,	,	PUNCT
ap-6836	267	1	b	b	X
ap-6836	267	2	−	−	NOUN
ap-6836	267	3	1	1	NUM
ap-6836	267	4	}	}	PUNCT
ap-6836	267	5	.	.	PUNCT
ap-6836	268	1	the	the	DET
ap-6836	268	2	antipalindromic	antipalindromic	ADJ
ap-6836	268	3	complement	complement	NOUN
ap-6836	268	4	of	of	ADP
ap-6836	268	5	u	u	NOUN
ap-6836	268	6	in	in	ADP
ap-6836	268	7	base	base	PROPN
ap-6836	268	8	b	b	PROPN
ap-6836	268	9	is	be	AUX
ap-6836	268	10	a(u	a(u	X
ap-6836	268	11	)	)	PUNCT
ap-6836	269	1	=	=	SYM
ap-6836	269	2	(	(	PUNCT
ap-6836	269	3	b−	b−	NOUN
ap-6836	269	4	1−	1−	NUM
ap-6836	269	5	un)(b−	un)(b−	ADJ
ap-6836	269	6	1−	1−	NUM
ap-6836	269	7	un−1	un−1	PROPN
ap-6836	269	8	)	)	PUNCT
ap-6836	269	9	.	.	PUNCT
ap-6836	269	10	.	.	PUNCT
ap-6836	269	11	.	.	PUNCT
ap-6836	270	1	(	(	PUNCT
ap-6836	270	2	b−	b−	PROPN
ap-6836	270	3	1−	1−	NUM
ap-6836	270	4	u0	u0	PROPN
ap-6836	270	5	)	)	PUNCT
ap-6836	270	6	.	.	PUNCT
ap-6836	271	1	theorem	theorem	NOUN
ap-6836	271	2	15	15	NUM
ap-6836	271	3	.	.	PUNCT
ap-6836	272	1	let	let	VERB
ap-6836	272	2	b	b	PROPN
ap-6836	272	3	∈	∈	PROPN
ap-6836	272	4	n	n	CCONJ
ap-6836	272	5	,	,	PUNCT
ap-6836	272	6	b	b	PROPN
ap-6836	272	7	≥	≥	NUM
ap-6836	272	8	2	2	NUM
ap-6836	272	9	.	.	PUNCT
ap-6836	273	1	an	an	DET
ap-6836	273	2	antipalindromic	antipalindromic	ADJ
ap-6836	273	3	number	number	NOUN
ap-6836	273	4	m	m	VERB
ap-6836	273	5	in	in	ADP
ap-6836	273	6	base	base	NOUN
ap-6836	273	7	bn	bn	NOUN
ap-6836	273	8	,	,	PUNCT
ap-6836	273	9	where	where	SCONJ
ap-6836	273	10	(	(	PUNCT
ap-6836	273	11	m)bn	m)bn	PROPN
ap-6836	273	12	=	=	SYM
ap-6836	273	13	uk	uk	PROPN
ap-6836	273	14	.	.	PUNCT
ap-6836	273	15	.	.	PUNCT
ap-6836	273	16	.	.	PUNCT
ap-6836	274	1	u1u0	u1u0	PROPN
ap-6836	274	2	and	and	CCONJ
ap-6836	274	3	uk	uk	PROPN
ap-6836	274	4	≥	≥	PRON
ap-6836	274	5	bn−1	bn−1	ADJ
ap-6836	274	6	,	,	PUNCT
ap-6836	274	7	is	be	AUX
ap-6836	274	8	simultaneously	simultaneously	ADV
ap-6836	274	9	antipalindromic	antipalindromic	ADJ
ap-6836	274	10	in	in	ADP
ap-6836	274	11	base	base	PROPN
ap-6836	274	12	b	b	PROPN
ap-6836	275	1	if	if	SCONJ
ap-6836	276	1	and	and	CCONJ
ap-6836	276	2	only	only	ADV
ap-6836	276	3	if	if	SCONJ
ap-6836	276	4	the	the	DET
ap-6836	276	5	expansion	expansion	NOUN
ap-6836	276	6	of	of	ADP
ap-6836	276	7	uj	uj	PROPN
ap-6836	276	8	in	in	ADP
ap-6836	276	9	base	base	PROPN
ap-6836	276	10	b	b	PROPN
ap-6836	276	11	of	of	ADP
ap-6836	276	12	length	length	NOUN
ap-6836	276	13	n	n	CCONJ
ap-6836	276	14	(	(	PUNCT
ap-6836	276	15	i.e.	i.e.	X
ap-6836	276	16	,	,	PUNCT
ap-6836	276	17	completed	complete	VERB
ap-6836	276	18	with	with	ADP
ap-6836	276	19	zeroes	zero	NOUN
ap-6836	276	20	if	if	SCONJ
ap-6836	276	21	necessary	necessary	ADJ
ap-6836	276	22	)	)	PUNCT
ap-6836	276	23	is	be	AUX
ap-6836	276	24	a	a	DET
ap-6836	276	25	palindrome	palindrome	NOUN
ap-6836	276	26	for	for	ADP
ap-6836	276	27	all	all	DET
ap-6836	276	28	j	j	PROPN
ap-6836	276	29	∈	∈	PROPN
ap-6836	276	30	{	{	PUNCT
ap-6836	276	31	0	0	NUM
ap-6836	276	32	,	,	PUNCT
ap-6836	276	33	1	1	NUM
ap-6836	276	34	,	,	PUNCT
ap-6836	276	35	.	.	PUNCT
ap-6836	276	36	.	.	PUNCT
ap-6836	277	1	.	.	PUNCT
ap-6836	278	1	,	,	PUNCT
ap-6836	278	2	k	k	X
ap-6836	278	3	}	}	PUNCT
ap-6836	278	4	.	.	PUNCT
ap-6836	279	1	432	432	NUM
ap-6836	279	2	vol	vol	NOUN
ap-6836	279	3	.	.	PUNCT
ap-6836	279	4	61	61	NUM
ap-6836	279	5	no	no	NOUN
ap-6836	279	6	.	.	PUNCT
ap-6836	280	1	3/2021	3/2021	NUM
ap-6836	280	2	antipalindromic	antipalindromic	ADJ
ap-6836	280	3	numbers	number	NOUN
ap-6836	280	4	proof	proof	NOUN
ap-6836	280	5	.	.	PUNCT
ap-6836	281	1	the	the	DET
ap-6836	281	2	digits	digit	NOUN
ap-6836	281	3	of	of	ADP
ap-6836	281	4	m	m	PROPN
ap-6836	281	5	in	in	ADP
ap-6836	281	6	base	base	NOUN
ap-6836	281	7	bn	bn	ADP
ap-6836	281	8	satisfy	satisfy	NOUN
ap-6836	281	9	0	0	NUM
ap-6836	281	10	≤	≤	PROPN
ap-6836	281	11	uj	uj	X
ap-6836	281	12	≤	≤	PROPN
ap-6836	281	13	bn	bn	ADP
ap-6836	281	14	−	−	PROPN
ap-6836	282	1	1	1	NUM
ap-6836	282	2	.	.	PUNCT
ap-6836	282	3	let	let	VERB
ap-6836	282	4	us	we	PRON
ap-6836	282	5	denote	denote	VERB
ap-6836	282	6	the	the	DET
ap-6836	282	7	expansion	expansion	NOUN
ap-6836	282	8	of	of	ADP
ap-6836	282	9	uj	uj	PROPN
ap-6836	282	10	in	in	ADP
ap-6836	282	11	base	base	PROPN
ap-6836	282	12	b	b	PROPN
ap-6836	282	13	by	by	ADP
ap-6836	282	14	(	(	PUNCT
ap-6836	282	15	uj)b	uj)b	PROPN
ap-6836	282	16	=	=	SYM
ap-6836	282	17	vj	vj	PROPN
ap-6836	282	18	,	,	PUNCT
ap-6836	282	19	n−1	n−1	PROPN
ap-6836	282	20	.	.	PUNCT
ap-6836	282	21	.	.	PUNCT
ap-6836	282	22	.	.	PUNCT
ap-6836	283	1	vj,1vj,0	vj,1vj,0	PUNCT
ap-6836	284	1	(	(	PUNCT
ap-6836	284	2	where	where	SCONJ
ap-6836	284	3	the	the	DET
ap-6836	284	4	expansion	expansion	NOUN
ap-6836	284	5	of	of	ADP
ap-6836	284	6	uj	uj	PROPN
ap-6836	284	7	in	in	ADP
ap-6836	284	8	base	base	PROPN
ap-6836	284	9	b	b	PROPN
ap-6836	284	10	is	be	AUX
ap-6836	284	11	completed	complete	VERB
ap-6836	284	12	with	with	ADP
ap-6836	284	13	zeroes	zero	NOUN
ap-6836	284	14	in	in	ADP
ap-6836	284	15	order	order	NOUN
ap-6836	284	16	to	to	PART
ap-6836	284	17	have	have	AUX
ap-6836	284	18	the	the	DET
ap-6836	284	19	length	length	NOUN
ap-6836	284	20	n	n	NOUN
ap-6836	284	21	if	if	SCONJ
ap-6836	284	22	necessary	necessary	ADJ
ap-6836	284	23	)	)	PUNCT
ap-6836	284	24	.	.	PUNCT
ap-6836	285	1	the	the	DET
ap-6836	285	2	antipalindromic	antipalindromic	PROPN
ap-6836	285	3	complement	complement	PROPN
ap-6836	285	4	a(uj	a(uj	PROPN
ap-6836	285	5	)	)	PUNCT
ap-6836	285	6	of	of	ADP
ap-6836	285	7	uj	uj	PROPN
ap-6836	285	8	in	in	ADP
ap-6836	285	9	base	base	NOUN
ap-6836	285	10	bn	bn	PROPN
ap-6836	285	11	equals	equal	VERB
ap-6836	285	12	bn	bn	INTJ
ap-6836	285	13	−	−	NUM
ap-6836	285	14	1	1	NUM
ap-6836	285	15	−	−	PROPN
ap-6836	285	16	uj	uj	PROPN
ap-6836	285	17	and	and	CCONJ
ap-6836	285	18	its	its	PRON
ap-6836	285	19	expansion	expansion	NOUN
ap-6836	285	20	in	in	ADP
ap-6836	285	21	base	base	PROPN
ap-6836	285	22	b	b	PROPN
ap-6836	285	23	equals	equal	VERB
ap-6836	285	24	(	(	PUNCT
ap-6836	285	25	a(uj))b	a(uj))b	NOUN
ap-6836	285	26	=	=	SYM
ap-6836	285	27	(	(	PUNCT
ap-6836	285	28	b−	b−	PROPN
ap-6836	285	29	1−	1−	NUM
ap-6836	285	30	vj	vj	PROPN
ap-6836	285	31	,	,	PUNCT
ap-6836	285	32	n−1	n−1	PROPN
ap-6836	285	33	)	)	PUNCT
ap-6836	285	34	.	.	PUNCT
ap-6836	285	35	.	.	PUNCT
ap-6836	285	36	.	.	PUNCT
ap-6836	286	1	(	(	PUNCT
ap-6836	286	2	b−	b−	PROPN
ap-6836	286	3	1−	1−	NUM
ap-6836	286	4	vj,1)(b−	vj,1)(b−	PROPN
ap-6836	286	5	1−	1−	NUM
ap-6836	286	6	vj,0	vj,0	PROPN
ap-6836	286	7	)	)	PUNCT
ap-6836	286	8	.	.	PUNCT
ap-6836	287	1	since	since	SCONJ
ap-6836	287	2	m	m	PROPN
ap-6836	287	3	is	be	AUX
ap-6836	287	4	antipalindromic	antipalindromic	ADJ
ap-6836	287	5	in	in	ADP
ap-6836	287	6	base	base	NOUN
ap-6836	287	7	bn	bn	NOUN
ap-6836	287	8	,	,	PUNCT
ap-6836	287	9	we	we	PRON
ap-6836	287	10	have	have	VERB
ap-6836	287	11	uk−j	uk−j	NOUN
ap-6836	287	12	=	=	SYM
ap-6836	287	13	a(uj	a(uj	PROPN
ap-6836	287	14	)	)	PUNCT
ap-6836	288	1	=	=	SYM
ap-6836	289	1	bn	bn	NUM
ap-6836	289	2	−	−	PROPN
ap-6836	289	3	1−	1−	NUM
ap-6836	289	4	uj	uj	PROPN
ap-6836	289	5	for	for	ADP
ap-6836	289	6	all	all	DET
ap-6836	289	7	j	j	PROPN
ap-6836	289	8	∈	∈	PROPN
ap-6836	289	9	{	{	PUNCT
ap-6836	289	10	0	0	NUM
ap-6836	289	11	,	,	PUNCT
ap-6836	289	12	1	1	NUM
ap-6836	289	13	,	,	PUNCT
ap-6836	289	14	.	.	PUNCT
ap-6836	289	15	.	.	PUNCT
ap-6836	289	16	.	.	PUNCT
ap-6836	290	1	,	,	PUNCT
ap-6836	290	2	k	k	X
ap-6836	290	3	}	}	PUNCT
ap-6836	290	4	.	.	PUNCT
ap-6836	291	1	let	let	VERB
ap-6836	291	2	us	we	PRON
ap-6836	291	3	now	now	ADV
ap-6836	291	4	consider	consider	VERB
ap-6836	291	5	the	the	DET
ap-6836	291	6	expansion	expansion	NOUN
ap-6836	291	7	of	of	ADP
ap-6836	291	8	m	m	PROPN
ap-6836	291	9	in	in	ADP
ap-6836	291	10	base	base	PROPN
ap-6836	291	11	b	b	NOUN
ap-6836	291	12	:	:	PUNCT
ap-6836	291	13	it	it	PRON
ap-6836	291	14	is	be	AUX
ap-6836	291	15	obtained	obtain	VERB
ap-6836	291	16	by	by	ADP
ap-6836	291	17	concatenation	concatenation	NOUN
ap-6836	291	18	of	of	ADP
ap-6836	291	19	the	the	DET
ap-6836	291	20	expansions	expansion	NOUN
ap-6836	291	21	of	of	ADP
ap-6836	291	22	uj	uj	PROPN
ap-6836	291	23	in	in	ADP
ap-6836	291	24	base	base	PROPN
ap-6836	291	25	b	b	PROPN
ap-6836	291	26	for	for	ADP
ap-6836	291	27	j	j	PROPN
ap-6836	291	28	∈	∈	PROPN
ap-6836	291	29	{	{	PUNCT
ap-6836	291	30	0	0	NUM
ap-6836	291	31	,	,	PUNCT
ap-6836	291	32	1	1	NUM
ap-6836	291	33	,	,	PUNCT
ap-6836	291	34	.	.	PUNCT
ap-6836	291	35	.	.	PUNCT
ap-6836	292	1	.	.	PUNCT
ap-6836	293	1	,	,	PUNCT
ap-6836	293	2	k	k	X
ap-6836	293	3	}	}	PUNCT
ap-6836	293	4	,	,	PUNCT
ap-6836	293	5	i.e.	i.e.	X
ap-6836	293	6	,	,	PUNCT
ap-6836	293	7	(	(	PUNCT
ap-6836	293	8	m)b	m)b	NOUN
ap-6836	293	9	=	=	PUNCT
ap-6836	293	10	(	(	PUNCT
ap-6836	293	11	uk)b	uk)b	PROPN
ap-6836	293	12	.	.	PUNCT
ap-6836	293	13	.	.	PUNCT
ap-6836	293	14	.	.	PUNCT
ap-6836	294	1	(	(	PUNCT
ap-6836	294	2	u1)b(u0)b	u1)b(u0)b	ADJ
ap-6836	294	3	.	.	PUNCT
ap-6836	295	1	following	follow	VERB
ap-6836	295	2	the	the	DET
ap-6836	295	3	assertion	assertion	NOUN
ap-6836	295	4	that	that	SCONJ
ap-6836	295	5	uk	uk	PROPN
ap-6836	295	6	≥	≥	PRON
ap-6836	295	7	bn−1	bn−1	ADJ
ap-6836	295	8	,	,	PUNCT
ap-6836	295	9	the	the	DET
ap-6836	295	10	expansion	expansion	NOUN
ap-6836	295	11	(	(	PUNCT
ap-6836	295	12	uk)b	uk)b	PROPN
ap-6836	295	13	starts	start	VERB
ap-6836	295	14	in	in	ADP
ap-6836	295	15	a	a	DET
ap-6836	295	16	non	non	ADJ
ap-6836	295	17	-	-	NOUN
ap-6836	295	18	zero	zero	NUM
ap-6836	295	19	.	.	PUNCT
ap-6836	296	1	thus	thus	ADV
ap-6836	296	2	,	,	PUNCT
ap-6836	296	3	the	the	DET
ap-6836	296	4	length	length	NOUN
ap-6836	296	5	of	of	ADP
ap-6836	296	6	the	the	DET
ap-6836	296	7	expansion	expansion	NOUN
ap-6836	296	8	(	(	PUNCT
ap-6836	296	9	m)b	m)b	NOUN
ap-6836	296	10	equals	equal	VERB
ap-6836	296	11	n	n	PRON
ap-6836	296	12	·	·	PUNCT
ap-6836	296	13	|(m)bn	|(m)bn	PROPN
ap-6836	296	14	|	|	NOUN
ap-6836	296	15	.	.	PUNCT
ap-6836	297	1	the	the	DET
ap-6836	297	2	number	number	NOUN
ap-6836	297	3	m	m	VERB
ap-6836	297	4	is	be	AUX
ap-6836	297	5	antipalindromic	antipalindromic	ADJ
ap-6836	297	6	in	in	ADP
ap-6836	297	7	base	base	PROPN
ap-6836	297	8	b	b	PROPN
ap-6836	298	1	if	if	SCONJ
ap-6836	298	2	and	and	CCONJ
ap-6836	298	3	only	only	ADV
ap-6836	298	4	if	if	SCONJ
ap-6836	298	5	(	(	PUNCT
ap-6836	298	6	uk−j)b	uk−j)b	PROPN
ap-6836	298	7	=	=	SYM
ap-6836	298	8	a((uj)b	a((uj)b	NOUN
ap-6836	298	9	)	)	PUNCT
ap-6836	298	10	for	for	ADP
ap-6836	298	11	all	all	DET
ap-6836	298	12	j	j	PROPN
ap-6836	298	13	∈	∈	PROPN
ap-6836	298	14	{	{	PUNCT
ap-6836	298	15	0	0	NUM
ap-6836	298	16	,	,	PUNCT
ap-6836	298	17	1	1	NUM
ap-6836	298	18	,	,	PUNCT
ap-6836	298	19	.	.	PUNCT
ap-6836	298	20	.	.	PUNCT
ap-6836	298	21	.	.	PUNCT
ap-6836	299	1	,	,	PUNCT
ap-6836	299	2	k	k	X
ap-6836	299	3	}	}	PUNCT
ap-6836	299	4	,	,	PUNCT
ap-6836	299	5	i.e.	i.e.	X
ap-6836	299	6	,	,	PUNCT
ap-6836	299	7	(	(	PUNCT
ap-6836	299	8	b−	b−	PROPN
ap-6836	299	9	1−	1−	NUM
ap-6836	299	10	vj	vj	PROPN
ap-6836	299	11	,	,	PUNCT
ap-6836	299	12	n−1	n−1	PROPN
ap-6836	299	13	)	)	PUNCT
ap-6836	299	14	.	.	PUNCT
ap-6836	299	15	.	.	PUNCT
ap-6836	299	16	.	.	PUNCT
ap-6836	300	1	(	(	PUNCT
ap-6836	300	2	b−	b−	PROPN
ap-6836	300	3	1−	1−	NUM
ap-6836	300	4	vj,1)(b−	vj,1)(b−	PROPN
ap-6836	300	5	1−	1−	NUM
ap-6836	300	6	vj,0	vj,0	PROPN
ap-6836	300	7	)	)	PUNCT
ap-6836	300	8	=	=	PUNCT
ap-6836	301	1	=	=	PUNCT
ap-6836	301	2	a(vj	a(vj	NOUN
ap-6836	301	3	,	,	PUNCT
ap-6836	301	4	n−1	n−1	PROPN
ap-6836	301	5	.	.	PUNCT
ap-6836	301	6	.	.	PUNCT
ap-6836	301	7	.	.	PUNCT
ap-6836	302	1	vj,1vj,0	vj,1vj,0	X
ap-6836	302	2	)	)	PUNCT
ap-6836	303	1	=	=	SYM
ap-6836	303	2	=	=	SYM
ap-6836	303	3	(	(	PUNCT
ap-6836	303	4	b−	b−	PROPN
ap-6836	303	5	1−	1−	NUM
ap-6836	303	6	vj,0)(b−	vj,0)(b−	NOUN
ap-6836	303	7	1−	1−	NUM
ap-6836	303	8	vj,1	vj,1	NOUN
ap-6836	303	9	)	)	PUNCT
ap-6836	303	10	.	.	PUNCT
ap-6836	303	11	.	.	PUNCT
ap-6836	303	12	.	.	PUNCT
ap-6836	304	1	(	(	PUNCT
ap-6836	304	2	b−	b−	PROPN
ap-6836	304	3	1−	1−	NUM
ap-6836	304	4	vj	vj	PROPN
ap-6836	304	5	,	,	PUNCT
ap-6836	304	6	n−1	n−1	PROPN
ap-6836	304	7	)	)	PUNCT
ap-6836	304	8	.	.	PUNCT
ap-6836	305	1	consequently	consequently	ADV
ap-6836	305	2	,	,	PUNCT
ap-6836	305	3	m	m	VERB
ap-6836	305	4	is	be	AUX
ap-6836	305	5	antipalindromic	antipalindromic	ADJ
ap-6836	305	6	in	in	ADP
ap-6836	305	7	base	base	PROPN
ap-6836	305	8	b	b	PROPN
ap-6836	306	1	if	if	SCONJ
ap-6836	306	2	and	and	CCONJ
ap-6836	306	3	only	only	ADV
ap-6836	306	4	if	if	SCONJ
ap-6836	306	5	(	(	PUNCT
ap-6836	306	6	uj)b	uj)b	NOUN
ap-6836	306	7	=	=	SYM
ap-6836	306	8	vj	vj	PROPN
ap-6836	306	9	,	,	PUNCT
ap-6836	306	10	n−1	n−1	PROPN
ap-6836	306	11	.	.	PUNCT
ap-6836	306	12	.	.	PUNCT
ap-6836	306	13	.	.	PUNCT
ap-6836	307	1	vj,1vj,0	vj,1vj,0	PROPN
ap-6836	307	2	is	be	AUX
ap-6836	307	3	a	a	DET
ap-6836	307	4	palindrome	palindrome	NOUN
ap-6836	307	5	for	for	ADP
ap-6836	307	6	all	all	DET
ap-6836	307	7	j	j	PROPN
ap-6836	307	8	∈	∈	PROPN
ap-6836	307	9	{	{	PUNCT
ap-6836	307	10	0	0	NUM
ap-6836	307	11	,	,	PUNCT
ap-6836	307	12	1	1	NUM
ap-6836	307	13	,	,	PUNCT
ap-6836	307	14	.	.	PUNCT
ap-6836	307	15	.	.	PUNCT
ap-6836	308	1	.	.	PUNCT
ap-6836	309	1	,	,	PUNCT
ap-6836	309	2	k	k	X
ap-6836	309	3	}	}	PUNCT
ap-6836	309	4	.	.	PUNCT
ap-6836	309	5	example	example	NOUN
ap-6836	310	1	6	6	NUM
ap-6836	310	2	.	.	PUNCT
ap-6836	310	3	consider	consider	VERB
ap-6836	310	4	m	m	NOUN
ap-6836	310	5	=	=	NOUN
ap-6836	310	6	73652	73652	NUM
ap-6836	310	7	.	.	PUNCT
ap-6836	311	1	then	then	ADV
ap-6836	311	2	(	(	PUNCT
ap-6836	311	3	m)27	m)27	NOUN
ap-6836	311	4	=	=	SYM
ap-6836	311	5	(	(	PUNCT
ap-6836	311	6	3)(20)(6)(23	3)(20)(6)(23	NUM
ap-6836	311	7	)	)	PUNCT
ap-6836	311	8	=	=	SYM
ap-6836	311	9	u3u2u1u0	u3u2u1u0	PROPN
ap-6836	311	10	,	,	PUNCT
ap-6836	311	11	thus	thus	ADV
ap-6836	311	12	,	,	PUNCT
ap-6836	311	13	m	m	VERB
ap-6836	311	14	is	be	AUX
ap-6836	311	15	antipalindromic	antipalindromic	ADJ
ap-6836	311	16	in	in	ADP
ap-6836	311	17	base	base	NOUN
ap-6836	311	18	27	27	NUM
ap-6836	311	19	=	=	SYM
ap-6836	311	20	33	33	NUM
ap-6836	311	21	.	.	PUNCT
ap-6836	312	1	however	however	ADV
ap-6836	312	2	,	,	PUNCT
ap-6836	312	3	(	(	PUNCT
ap-6836	312	4	m)3	m)3	NOUN
ap-6836	312	5	=	=	SYM
ap-6836	312	6	10202020212	10202020212	NUM
ap-6836	312	7	,	,	PUNCT
ap-6836	312	8	thus	thus	ADV
ap-6836	312	9	m	m	NOUN
ap-6836	312	10	is	be	AUX
ap-6836	312	11	not	not	PART
ap-6836	312	12	antipalindromic	antipalindromic	ADJ
ap-6836	312	13	in	in	ADP
ap-6836	312	14	base	base	NOUN
ap-6836	312	15	3	3	NUM
ap-6836	312	16	.	.	PUNCT
ap-6836	313	1	if	if	SCONJ
ap-6836	313	2	we	we	PRON
ap-6836	313	3	cut	cut	VERB
ap-6836	313	4	(	(	PUNCT
ap-6836	313	5	m)3	m)3	NOUN
ap-6836	313	6	into	into	ADP
ap-6836	313	7	blocks	block	NOUN
ap-6836	313	8	of	of	ADP
ap-6836	313	9	length	length	NOUN
ap-6836	313	10	3	3	NUM
ap-6836	313	11	,	,	PUNCT
ap-6836	313	12	then	then	ADV
ap-6836	313	13	all	all	PRON
ap-6836	313	14	of	of	ADP
ap-6836	313	15	them	they	PRON
ap-6836	313	16	are	be	AUX
ap-6836	313	17	palindromic	palindromic	ADJ
ap-6836	313	18	.	.	PUNCT
ap-6836	314	1	however	however	ADV
ap-6836	314	2	,	,	PUNCT
ap-6836	314	3	the	the	DET
ap-6836	314	4	first	first	ADJ
ap-6836	314	5	one	one	NOUN
ap-6836	314	6	equals	equal	VERB
ap-6836	314	7	010	010	NUM
ap-6836	314	8	and	and	CCONJ
ap-6836	314	9	it	it	PRON
ap-6836	314	10	starts	start	VERB
ap-6836	314	11	with	with	ADP
ap-6836	314	12	a	a	DET
ap-6836	314	13	zero	zero	NUM
ap-6836	314	14	,	,	PUNCT
ap-6836	314	15	hence	hence	ADV
ap-6836	314	16	the	the	DET
ap-6836	314	17	assumption	assumption	NOUN
ap-6836	314	18	u3	u3	NOUN
ap-6836	314	19	≥	≥	NUM
ap-6836	314	20	9	9	NUM
ap-6836	314	21	of	of	ADP
ap-6836	314	22	theorem	theorem	NOUN
ap-6836	314	23	15	15	NUM
ap-6836	314	24	is	be	AUX
ap-6836	314	25	not	not	PART
ap-6836	314	26	met	meet	VERB
ap-6836	314	27	.	.	PUNCT
ap-6836	315	1	example	example	NOUN
ap-6836	315	2	7	7	NUM
ap-6836	315	3	.	.	X
ap-6836	315	4	consider	consider	VERB
ap-6836	315	5	b	b	NOUN
ap-6836	315	6	=	=	SYM
ap-6836	315	7	10	10	NUM
ap-6836	315	8	.	.	PUNCT
ap-6836	316	1	the	the	DET
ap-6836	316	2	number	number	NOUN
ap-6836	316	3	6633442277556633	6633442277556633	NUM
ap-6836	316	4	is	be	AUX
ap-6836	316	5	an	an	DET
ap-6836	316	6	antipalindromic	antipalindromic	ADJ
ap-6836	316	7	number	number	NOUN
ap-6836	316	8	both	both	PRON
ap-6836	316	9	in	in	ADP
ap-6836	316	10	base	base	NOUN
ap-6836	316	11	10	10	NUM
ap-6836	316	12	and	and	CCONJ
ap-6836	316	13	100	100	NUM
ap-6836	316	14	.	.	X
ap-6836	317	1	6	6	NUM
ap-6836	317	2	.	.	X
ap-6836	317	3	conclusion	conclusion	NOUN
ap-6836	317	4	and	and	CCONJ
ap-6836	317	5	open	open	ADJ
ap-6836	317	6	problems	problem	NOUN
ap-6836	317	7	in	in	ADP
ap-6836	317	8	this	this	DET
ap-6836	317	9	paper	paper	NOUN
ap-6836	317	10	,	,	PUNCT
ap-6836	317	11	we	we	PRON
ap-6836	317	12	carried	carry	VERB
ap-6836	317	13	out	out	ADP
ap-6836	317	14	a	a	DET
ap-6836	317	15	thorough	thorough	ADJ
ap-6836	317	16	study	study	NOUN
ap-6836	317	17	of	of	ADP
ap-6836	317	18	antipalindromic	antipalindromic	ADJ
ap-6836	317	19	numbers	number	NOUN
ap-6836	317	20	and	and	CCONJ
ap-6836	317	21	described	describe	VERB
ap-6836	317	22	known	know	VERB
ap-6836	317	23	results	result	NOUN
ap-6836	317	24	regarding	regard	VERB
ap-6836	317	25	palindromic	palindromic	ADJ
ap-6836	317	26	numbers	number	NOUN
ap-6836	317	27	in	in	ADP
ap-6836	317	28	order	order	NOUN
ap-6836	317	29	to	to	PART
ap-6836	317	30	draw	draw	VERB
ap-6836	317	31	a	a	DET
ap-6836	317	32	comparison	comparison	NOUN
ap-6836	317	33	.	.	PUNCT
ap-6836	318	1	it	it	PRON
ap-6836	318	2	brings	bring	VERB
ap-6836	318	3	a	a	DET
ap-6836	318	4	number	number	NOUN
ap-6836	318	5	of	of	ADP
ap-6836	318	6	new	new	ADJ
ap-6836	318	7	results	result	NOUN
ap-6836	318	8	:	:	PUNCT
ap-6836	318	9	•	•	X
ap-6836	318	10	we	we	PRON
ap-6836	318	11	described	describe	VERB
ap-6836	318	12	the	the	DET
ap-6836	318	13	divisibility	divisibility	NOUN
ap-6836	318	14	of	of	ADP
ap-6836	318	15	antipalindromic	antipalindromic	ADJ
ap-6836	318	16	numbers	number	NOUN
ap-6836	318	17	and	and	CCONJ
ap-6836	318	18	showed	show	VERB
ap-6836	318	19	that	that	SCONJ
ap-6836	318	20	non	non	ADJ
ap-6836	318	21	-	-	ADJ
ap-6836	318	22	trivial	trivial	ADJ
ap-6836	318	23	antipalindromic	antipalindromic	ADJ
ap-6836	318	24	primes	prime	NOUN
ap-6836	318	25	may	may	AUX
ap-6836	318	26	be	be	AUX
ap-6836	318	27	found	find	VERB
ap-6836	318	28	only	only	ADV
ap-6836	318	29	in	in	ADP
ap-6836	318	30	base	base	NOUN
ap-6836	318	31	3	3	NUM
ap-6836	318	32	.	.	NOUN
ap-6836	318	33	•	•	NOUN
ap-6836	318	34	we	we	PRON
ap-6836	318	35	found	find	VERB
ap-6836	318	36	several	several	ADJ
ap-6836	318	37	classes	class	NOUN
ap-6836	318	38	of	of	ADP
ap-6836	318	39	antipalindromic	antipalindromic	ADJ
ap-6836	318	40	squares	square	NOUN
ap-6836	318	41	and	and	CCONJ
ap-6836	318	42	higher	high	ADJ
ap-6836	318	43	powers	power	NOUN
ap-6836	318	44	.	.	PUNCT
ap-6836	319	1	•	•	ADV
ap-6836	319	2	we	we	PRON
ap-6836	319	3	described	describe	VERB
ap-6836	319	4	pairs	pair	NOUN
ap-6836	319	5	of	of	ADP
ap-6836	319	6	bases	basis	NOUN
ap-6836	319	7	such	such	ADJ
ap-6836	319	8	that	that	SCONJ
ap-6836	319	9	there	there	PRON
ap-6836	319	10	is	be	VERB
ap-6836	319	11	a	a	DET
ap-6836	319	12	number	number	NOUN
ap-6836	319	13	antipalindromic	antipalindromic	NOUN
ap-6836	319	14	in	in	ADP
ap-6836	319	15	both	both	PRON
ap-6836	319	16	of	of	ADP
ap-6836	319	17	these	these	DET
ap-6836	319	18	bases	basis	NOUN
ap-6836	319	19	.	.	PUNCT
ap-6836	320	1	moreover	moreover	ADV
ap-6836	320	2	,	,	PUNCT
ap-6836	320	3	we	we	PRON
ap-6836	320	4	obtained	obtain	VERB
ap-6836	320	5	the	the	DET
ap-6836	320	6	following	follow	VERB
ap-6836	320	7	interesting	interesting	ADJ
ap-6836	320	8	results	result	NOUN
ap-6836	320	9	concerning	concern	VERB
ap-6836	320	10	multi	multi	ADJ
ap-6836	320	11	-	-	ADJ
ap-6836	320	12	base	base	ADJ
ap-6836	320	13	antipalindromic	antipalindromic	ADJ
ap-6836	320	14	numbers	number	NOUN
ap-6836	320	15	:	:	PUNCT
ap-6836	320	16	.	.	PUNCT
ap-6836	321	1	for	for	ADP
ap-6836	321	2	any	any	DET
ap-6836	321	3	composite	composite	ADJ
ap-6836	321	4	number	number	NOUN
ap-6836	321	5	,	,	PUNCT
ap-6836	321	6	there	there	PRON
ap-6836	321	7	exist	exist	VERB
ap-6836	321	8	at	at	ADV
ap-6836	321	9	least	least	ADV
ap-6836	321	10	two	two	NUM
ap-6836	321	11	bases	basis	NOUN
ap-6836	321	12	such	such	ADJ
ap-6836	321	13	that	that	SCONJ
ap-6836	321	14	this	this	DET
ap-6836	321	15	number	number	NOUN
ap-6836	321	16	is	be	AUX
ap-6836	321	17	antipalindromic	antipalindromic	ADJ
ap-6836	321	18	in	in	ADP
ap-6836	321	19	both	both	PRON
ap-6836	321	20	of	of	ADP
ap-6836	321	21	them	they	PRON
ap-6836	321	22	.	.	PUNCT
ap-6836	321	23	.	.	PUNCT
ap-6836	322	1	for	for	ADP
ap-6836	322	2	every	every	DET
ap-6836	322	3	n	n	PRON
ap-6836	322	4	∈	∈	PROPN
ap-6836	322	5	n	n	CCONJ
ap-6836	322	6	,	,	PUNCT
ap-6836	322	7	there	there	PRON
ap-6836	322	8	exist	exist	VERB
ap-6836	322	9	infinitely	infinitely	ADV
ap-6836	322	10	many	many	ADJ
ap-6836	322	11	numbers	number	NOUN
ap-6836	322	12	that	that	PRON
ap-6836	322	13	are	be	AUX
ap-6836	322	14	antipalindromic	antipalindromic	ADJ
ap-6836	322	15	in	in	ADP
ap-6836	322	16	at	at	ADV
ap-6836	322	17	least	least	ADJ
ap-6836	322	18	n	n	PRON
ap-6836	322	19	bases	basis	NOUN
ap-6836	322	20	.	.	PUNCT
ap-6836	322	21	.	.	PUNCT
ap-6836	323	1	let	let	VERB
ap-6836	323	2	b	b	NOUN
ap-6836	323	3	∈	∈	PROPN
ap-6836	323	4	n	n	CCONJ
ap-6836	323	5	,	,	PUNCT
ap-6836	323	6	b	b	PROPN
ap-6836	323	7	≥	≥	NUM
ap-6836	323	8	2	2	NUM
ap-6836	323	9	.	.	PUNCT
ap-6836	324	1	then	then	ADV
ap-6836	324	2	there	there	PRON
ap-6836	324	3	exists	exist	VERB
ap-6836	324	4	m	m	VERB
ap-6836	324	5	∈	∈	PROPN
ap-6836	324	6	n	n	PRON
ap-6836	324	7	such	such	ADJ
ap-6836	324	8	that	that	SCONJ
ap-6836	324	9	m	m	PROPN
ap-6836	324	10	is	be	AUX
ap-6836	324	11	antipalindromic	antipalindromic	ADJ
ap-6836	324	12	in	in	ADP
ap-6836	324	13	base	base	PROPN
ap-6836	324	14	b	b	PROPN
ap-6836	324	15	and	and	CCONJ
ap-6836	324	16	in	in	ADP
ap-6836	324	17	at	at	ADV
ap-6836	324	18	least	least	ADV
ap-6836	324	19	one	one	NUM
ap-6836	324	20	more	more	ADJ
ap-6836	324	21	base	base	NOUN
ap-6836	324	22	less	less	ADJ
ap-6836	324	23	than	than	ADP
ap-6836	324	24	m.	m.	NOUN
ap-6836	324	25	this	this	DET
ap-6836	324	26	paper	paper	NOUN
ap-6836	324	27	is	be	AUX
ap-6836	324	28	based	base	VERB
ap-6836	324	29	on	on	ADP
ap-6836	324	30	the	the	DET
ap-6836	324	31	bachelor	bachelor	ADJ
ap-6836	324	32	thesis	thesis	NOUN
ap-6836	325	1	[	[	X
ap-6836	325	2	14	14	NUM
ap-6836	325	3	]	]	X
ap-6836	325	4	,	,	PUNCT
ap-6836	325	5	where	where	SCONJ
ap-6836	325	6	several	several	ADJ
ap-6836	325	7	more	more	ADJ
ap-6836	325	8	results	result	NOUN
ap-6836	325	9	were	be	AUX
ap-6836	325	10	obtained	obtain	VERB
ap-6836	325	11	:	:	PUNCT
ap-6836	325	12	•	•	ADP
ap-6836	325	13	the	the	DET
ap-6836	325	14	number	number	NOUN
ap-6836	325	15	of	of	ADP
ap-6836	325	16	(	(	PUNCT
ap-6836	325	17	anti)palindromic	anti)palindromic	ADJ
ap-6836	325	18	numbers	number	NOUN
ap-6836	325	19	of	of	ADP
ap-6836	325	20	a	a	DET
ap-6836	325	21	certain	certain	ADJ
ap-6836	325	22	length	length	NOUN
ap-6836	325	23	and	and	CCONJ
ap-6836	325	24	the	the	DET
ap-6836	325	25	maximum	maximum	ADJ
ap-6836	325	26	and	and	CCONJ
ap-6836	325	27	minimum	minimum	ADJ
ap-6836	325	28	number	number	NOUN
ap-6836	325	29	of	of	ADP
ap-6836	325	30	antipalindromic	antipalindromic	ADJ
ap-6836	325	31	numbers	number	NOUN
ap-6836	325	32	between	between	ADP
ap-6836	325	33	palindromic	palindromic	ADJ
ap-6836	325	34	numbers	number	NOUN
ap-6836	325	35	and	and	CCONJ
ap-6836	325	36	vice	vice	NOUN
ap-6836	325	37	versa	versa	ADV
ap-6836	325	38	;	;	PUNCT
ap-6836	325	39	•	•	ADP
ap-6836	325	40	an	an	DET
ap-6836	325	41	explicit	explicit	ADJ
ap-6836	325	42	formula	formula	NOUN
ap-6836	325	43	for	for	ADP
ap-6836	325	44	the	the	DET
ap-6836	325	45	length	length	NOUN
ap-6836	325	46	of	of	ADP
ap-6836	325	47	gaps	gap	NOUN
ap-6836	325	48	between	between	ADP
ap-6836	325	49	neighboring	neighbor	VERB
ap-6836	325	50	antipalindromic	antipalindromic	ADJ
ap-6836	325	51	numbers	number	NOUN
ap-6836	325	52	.	.	PUNCT
ap-6836	326	1	we	we	PRON
ap-6836	326	2	created	create	VERB
ap-6836	326	3	a	a	DET
ap-6836	326	4	user	user	NOUN
ap-6836	326	5	-	-	PUNCT
ap-6836	326	6	friendly	friendly	ADJ
ap-6836	326	7	application	application	NOUN
ap-6836	326	8	for	for	ADP
ap-6836	326	9	all	all	DET
ap-6836	326	10	the	the	DET
ap-6836	326	11	questions	question	NOUN
ap-6836	326	12	studied	study	VERB
ap-6836	326	13	[	[	PUNCT
ap-6836	326	14	9	9	NUM
ap-6836	326	15	]	]	PUNCT
ap-6836	326	16	,	,	PUNCT
ap-6836	326	17	which	which	PRON
ap-6836	326	18	is	be	AUX
ap-6836	326	19	freely	freely	ADV
ap-6836	326	20	available	available	ADJ
ap-6836	326	21	to	to	ADP
ap-6836	326	22	the	the	DET
ap-6836	326	23	reader	reader	NOUN
ap-6836	326	24	.	.	PUNCT
ap-6836	327	1	based	base	VERB
ap-6836	327	2	on	on	ADP
ap-6836	327	3	computer	computer	NOUN
ap-6836	327	4	experiments	experiment	NOUN
ap-6836	327	5	,	,	PUNCT
ap-6836	327	6	we	we	PRON
ap-6836	327	7	state	state	VERB
ap-6836	327	8	the	the	DET
ap-6836	327	9	following	follow	VERB
ap-6836	327	10	conjectures	conjecture	NOUN
ap-6836	327	11	and	and	CCONJ
ap-6836	327	12	open	open	ADJ
ap-6836	327	13	problems	problem	NOUN
ap-6836	327	14	:	:	PUNCT
ap-6836	327	15	(	(	PUNCT
ap-6836	327	16	1	1	X
ap-6836	327	17	.	.	PUNCT
ap-6836	327	18	)	)	PUNCT
ap-6836	327	19	are	be	AUX
ap-6836	327	20	there	there	ADV
ap-6836	327	21	infinitely	infinitely	ADV
ap-6836	327	22	many	many	ADJ
ap-6836	327	23	antipalindromic	antipalindromic	ADJ
ap-6836	327	24	primes	prime	NOUN
ap-6836	327	25	in	in	ADP
ap-6836	327	26	base	base	NOUN
ap-6836	327	27	3	3	NUM
ap-6836	327	28	?	?	PUNCT
ap-6836	328	1	(	(	PUNCT
ap-6836	328	2	we	we	PRON
ap-6836	328	3	know	know	VERB
ap-6836	328	4	there	there	PRON
ap-6836	328	5	is	be	VERB
ap-6836	328	6	never	never	ADV
ap-6836	328	7	more	more	ADJ
ap-6836	328	8	than	than	ADP
ap-6836	328	9	one	one	NUM
ap-6836	328	10	antipalindromic	antipalindromic	ADJ
ap-6836	328	11	prime	prime	NOUN
ap-6836	328	12	in	in	ADP
ap-6836	328	13	any	any	DET
ap-6836	328	14	other	other	ADJ
ap-6836	328	15	base	base	NOUN
ap-6836	328	16	except	except	SCONJ
ap-6836	328	17	for	for	ADP
ap-6836	328	18	3	3	NUM
ap-6836	328	19	.	.	PUNCT
ap-6836	328	20	)	)	PUNCT
ap-6836	328	21	during	during	ADP
ap-6836	328	22	an	an	DET
ap-6836	328	23	extended	extended	ADJ
ap-6836	328	24	search	search	NOUN
ap-6836	328	25	,	,	PUNCT
ap-6836	328	26	the	the	DET
ap-6836	328	27	first	first	ADJ
ap-6836	328	28	637807	637807	NUM
ap-6836	328	29	antipalindromic	antipalindromic	ADJ
ap-6836	328	30	primes	prime	NOUN
ap-6836	328	31	have	have	AUX
ap-6836	328	32	been	be	AUX
ap-6836	328	33	found	find	VERB
ap-6836	328	34	.	.	PUNCT
ap-6836	329	1	(	(	PUNCT
ap-6836	329	2	2	2	NUM
ap-6836	329	3	.	.	PUNCT
ap-6836	329	4	)	)	PUNCT
ap-6836	330	1	we	we	PRON
ap-6836	330	2	conjecture	conjecture	VERB
ap-6836	330	3	it	it	PRON
ap-6836	330	4	is	be	AUX
ap-6836	330	5	possible	possible	ADJ
ap-6836	330	6	to	to	PART
ap-6836	330	7	express	express	VERB
ap-6836	330	8	any	any	DET
ap-6836	330	9	integer	integer	NOUN
ap-6836	330	10	number	number	NOUN
ap-6836	330	11	(	(	PUNCT
ap-6836	330	12	except	except	SCONJ
ap-6836	330	13	for	for	ADP
ap-6836	330	14	24	24	NUM
ap-6836	330	15	,	,	PUNCT
ap-6836	330	16	37	37	NUM
ap-6836	330	17	,	,	PUNCT
ap-6836	330	18	49	49	NUM
ap-6836	330	19	,	,	PUNCT
ap-6836	330	20	117	117	NUM
ap-6836	330	21	,	,	PUNCT
ap-6836	330	22	and	and	CCONJ
ap-6836	330	23	421	421	NUM
ap-6836	330	24	)	)	PUNCT
ap-6836	330	25	as	as	ADP
ap-6836	330	26	the	the	DET
ap-6836	330	27	sum	sum	NOUN
ap-6836	330	28	of	of	ADP
ap-6836	330	29	at	at	ADV
ap-6836	330	30	most	most	ADV
ap-6836	330	31	three	three	NUM
ap-6836	330	32	antipalindromic	antipalindromic	ADJ
ap-6836	330	33	numbers	number	NOUN
ap-6836	330	34	in	in	ADP
ap-6836	330	35	base	base	NOUN
ap-6836	330	36	3	3	NUM
ap-6836	330	37	.	.	PUNCT
ap-6836	331	1	our	our	PRON
ap-6836	331	2	computer	computer	NOUN
ap-6836	331	3	program	program	NOUN
ap-6836	331	4	shows	show	VERB
ap-6836	331	5	that	that	SCONJ
ap-6836	331	6	the	the	DET
ap-6836	331	7	answer	answer	NOUN
ap-6836	331	8	is	be	AUX
ap-6836	331	9	positive	positive	ADJ
ap-6836	331	10	up	up	ADP
ap-6836	331	11	to	to	ADP
ap-6836	331	12	5	5	NUM
ap-6836	331	13	·	·	SYM
ap-6836	331	14	106	106	NUM
ap-6836	331	15	.	.	PUNCT
ap-6836	332	1	(	(	PUNCT
ap-6836	332	2	3	3	NUM
ap-6836	332	3	.	.	PUNCT
ap-6836	332	4	)	)	PUNCT
ap-6836	333	1	we	we	PRON
ap-6836	333	2	conjecture	conjecture	VERB
ap-6836	333	3	it	it	PRON
ap-6836	333	4	is	be	AUX
ap-6836	333	5	possible	possible	ADJ
ap-6836	333	6	to	to	PART
ap-6836	333	7	express	express	VERB
ap-6836	333	8	any	any	DET
ap-6836	333	9	palindromic	palindromic	ADJ
ap-6836	333	10	number	number	NOUN
ap-6836	333	11	in	in	ADP
ap-6836	333	12	base	base	NOUN
ap-6836	333	13	3	3	NUM
ap-6836	333	14	as	as	ADP
ap-6836	333	15	the	the	DET
ap-6836	333	16	sum	sum	NOUN
ap-6836	333	17	of	of	ADP
ap-6836	333	18	at	at	ADV
ap-6836	333	19	most	most	ADV
ap-6836	333	20	three	three	NUM
ap-6836	333	21	antipalindromic	antipalindromic	ADJ
ap-6836	333	22	numbers	number	NOUN
ap-6836	333	23	in	in	ADP
ap-6836	333	24	base	base	NOUN
ap-6836	333	25	3	3	NUM
ap-6836	333	26	.	.	PUNCT
ap-6836	334	1	this	this	DET
ap-6836	334	2	conjecture	conjecture	NOUN
ap-6836	334	3	follows	follow	VERB
ap-6836	334	4	evidently	evidently	ADV
ap-6836	334	5	from	from	ADP
ap-6836	334	6	the	the	DET
ap-6836	334	7	previous	previous	ADJ
ap-6836	334	8	one	one	NUM
ap-6836	334	9	,	,	PUNCT
ap-6836	334	10	and	and	CCONJ
ap-6836	334	11	we	we	PRON
ap-6836	334	12	verified	verify	VERB
ap-6836	334	13	it	it	PRON
ap-6836	334	14	even	even	ADV
ap-6836	334	15	for	for	ADP
ap-6836	334	16	larger	large	ADJ
ap-6836	334	17	numbers	number	NOUN
ap-6836	334	18	,	,	PUNCT
ap-6836	334	19	up	up	ADP
ap-6836	334	20	to	to	ADP
ap-6836	334	21	108	108	NUM
ap-6836	334	22	.	.	PUNCT
ap-6836	335	1	(	(	PUNCT
ap-6836	335	2	4	4	NUM
ap-6836	335	3	.	.	PUNCT
ap-6836	335	4	)	)	PUNCT
ap-6836	335	5	is	be	AUX
ap-6836	335	6	there	there	PRON
ap-6836	335	7	a	a	DET
ap-6836	335	8	pair	pair	NOUN
ap-6836	335	9	of	of	ADP
ap-6836	335	10	bases	basis	NOUN
ap-6836	335	11	such	such	ADJ
ap-6836	335	12	that	that	SCONJ
ap-6836	335	13	it	it	PRON
ap-6836	335	14	is	be	AUX
ap-6836	335	15	impossible	impossible	ADJ
ap-6836	335	16	to	to	PART
ap-6836	335	17	find	find	VERB
ap-6836	335	18	any	any	DET
ap-6836	335	19	number	number	NOUN
ap-6836	335	20	that	that	PRON
ap-6836	335	21	has	have	VERB
ap-6836	335	22	an	an	DET
ap-6836	335	23	antipalindromic	antipalindromic	ADJ
ap-6836	335	24	expansion	expansion	NOUN
ap-6836	335	25	in	in	ADP
ap-6836	335	26	both	both	PRON
ap-6836	335	27	of	of	ADP
ap-6836	335	28	them	they	PRON
ap-6836	335	29	?	?	PUNCT
ap-6836	336	1	according	accord	VERB
ap-6836	336	2	to	to	ADP
ap-6836	336	3	our	our	PRON
ap-6836	336	4	computer	computer	NOUN
ap-6836	336	5	experiments	experiment	NOUN
ap-6836	336	6	,	,	PUNCT
ap-6836	336	7	suitable	suitable	ADJ
ap-6836	336	8	candidates	candidate	NOUN
ap-6836	336	9	seem	seem	VERB
ap-6836	336	10	to	to	PART
ap-6836	336	11	be	be	AUX
ap-6836	336	12	the	the	DET
ap-6836	336	13	bases	basis	NOUN
ap-6836	336	14	6	6	NUM
ap-6836	336	15	and	and	CCONJ
ap-6836	336	16	8	8	NUM
ap-6836	336	17	.	.	PUNCT
ap-6836	337	1	it	it	PRON
ap-6836	337	2	is	be	AUX
ap-6836	337	3	to	to	PART
ap-6836	337	4	be	be	AUX
ap-6836	337	5	studied	study	VERB
ap-6836	337	6	in	in	ADP
ap-6836	337	7	the	the	DET
ap-6836	337	8	future	future	NOUN
ap-6836	337	9	.	.	PUNCT
ap-6836	338	1	acknowledgements	acknowledgement	NOUN
ap-6836	338	2	we	we	PRON
ap-6836	338	3	would	would	AUX
ap-6836	338	4	like	like	VERB
ap-6836	338	5	to	to	PART
ap-6836	338	6	thank	thank	VERB
ap-6836	338	7	to	to	ADP
ap-6836	338	8	the	the	DET
ap-6836	338	9	reviewers	reviewer	NOUN
ap-6836	338	10	for	for	ADP
ap-6836	338	11	their	their	PRON
ap-6836	338	12	useful	useful	ADJ
ap-6836	338	13	comments	comment	NOUN
ap-6836	338	14	and	and	CCONJ
ap-6836	338	15	suitable	suitable	ADJ
ap-6836	338	16	suggestions	suggestion	NOUN
ap-6836	338	17	concerning	concern	VERB
ap-6836	338	18	references	reference	NOUN
ap-6836	338	19	.	.	PUNCT
ap-6836	339	1	l.	l.	PROPN
ap-6836	339	2	dvořáková	dvořáková	PROPN
ap-6836	339	3	received	receive	VERB
ap-6836	339	4	funding	funding	NOUN
ap-6836	339	5	from	from	ADP
ap-6836	339	6	the	the	DET
ap-6836	339	7	ministry	ministry	PROPN
ap-6836	339	8	of	of	ADP
ap-6836	339	9	education	education	PROPN
ap-6836	339	10	,	,	PUNCT
ap-6836	339	11	youth	youth	NOUN
ap-6836	339	12	and	and	CCONJ
ap-6836	339	13	sports	sport	NOUN
ap-6836	339	14	of	of	ADP
ap-6836	339	15	the	the	DET
ap-6836	339	16	czech	czech	PROPN
ap-6836	339	17	republic	republic	NOUN
ap-6836	339	18	through	through	ADP
ap-6836	339	19	the	the	DET
ap-6836	339	20	project	project	NOUN
ap-6836	339	21	no	no	INTJ
ap-6836	339	22	.	.	PUNCT
ap-6836	339	23	cz.02.1.01/0.0/0.0/16_019/0000778	cz.02.1.01/0.0/0.0/16_019/0000778	PROPN
ap-6836	339	24	.	.	PUNCT
ap-6836	340	1	references	reference	NOUN
ap-6836	340	2	[	[	X
ap-6836	340	3	1	1	X
ap-6836	340	4	]	]	PUNCT
ap-6836	340	5	j.	j.	PROPN
ap-6836	340	6	joyce	joyce	PROPN
ap-6836	340	7	.	.	PUNCT
ap-6836	341	1	ulysses	ulysses	PROPN
ap-6836	341	2	.	.	PUNCT
ap-6836	342	1	first	first	PROPN
ap-6836	342	2	edition	edition	PROPN
ap-6836	342	3	.	.	PUNCT
ap-6836	343	1	shakespeare	shakespeare	PROPN
ap-6836	343	2	and	and	CCONJ
ap-6836	343	3	company	company	NOUN
ap-6836	343	4	,	,	PUNCT
ap-6836	343	5	12	12	NUM
ap-6836	343	6	,	,	PUNCT
ap-6836	343	7	rue	rue	X
ap-6836	343	8	de	de	X
ap-6836	343	9	l’odéon	l’odéon	PROPN
ap-6836	343	10	,	,	PUNCT
ap-6836	343	11	paris	paris	PROPN
ap-6836	343	12	,	,	PUNCT
ap-6836	343	13	1922	1922	NUM
ap-6836	343	14	.	.	PUNCT
ap-6836	344	1	[	[	X
ap-6836	344	2	2	2	NUM
ap-6836	344	3	]	]	X
ap-6836	344	4	n.	n.	PROPN
ap-6836	344	5	j.	j.	PROPN
ap-6836	344	6	a.	a.	PROPN
ap-6836	344	7	sloane	sloane	PROPN
ap-6836	344	8	.	.	PUNCT
ap-6836	345	1	the	the	DET
ap-6836	345	2	on	on	ADP
ap-6836	345	3	-	-	PUNCT
ap-6836	345	4	line	line	NOUN
ap-6836	345	5	encyclopedia	encyclopedia	NOUN
ap-6836	345	6	of	of	ADP
ap-6836	345	7	integer	integer	NOUN
ap-6836	345	8	sequences	sequence	NOUN
ap-6836	345	9	.	.	PUNCT
ap-6836	346	1	https://oeis.org	https://oeis.org	PROPN
ap-6836	346	2	.	.	PUNCT
ap-6836	347	1	[	[	X
ap-6836	347	2	3	3	NUM
ap-6836	347	3	]	]	X
ap-6836	347	4	a.	a.	NOUN
ap-6836	347	5	tripathi	tripathi	PROPN
ap-6836	347	6	.	.	PUNCT
ap-6836	348	1	characterization	characterization	NOUN
ap-6836	348	2	and	and	CCONJ
ap-6836	348	3	enumeration	enumeration	NOUN
ap-6836	348	4	of	of	ADP
ap-6836	348	5	palindromic	palindromic	ADJ
ap-6836	348	6	numbers	number	NOUN
ap-6836	348	7	whose	whose	DET
ap-6836	348	8	squares	square	NOUN
ap-6836	348	9	are	be	AUX
ap-6836	348	10	also	also	ADV
ap-6836	348	11	palindromic	palindromic	ADJ
ap-6836	348	12	.	.	PUNCT
ap-6836	349	1	rocky	rocky	ADJ
ap-6836	349	2	mountain	mountain	PROPN
ap-6836	349	3	j	j	PROPN
ap-6836	349	4	math	math	PROPN
ap-6836	349	5	50(3):1115–1124	50(3):1115–1124	NUM
ap-6836	349	6	,	,	PUNCT
ap-6836	349	7	2020	2020	NUM
ap-6836	349	8	.	.	PUNCT
ap-6836	350	1	https://doi.org/10.1216/rmj.2020.50.1115	https://doi.org/10.1216/rmj.2020.50.1115	NOUN
ap-6836	350	2	.	.	PUNCT
ap-6836	351	1	433	433	NUM
ap-6836	351	2	https://oeis.org	https://oeis.org	PROPN
ap-6836	351	3	https://doi.org/10.1216/rmj.2020.50.1115	https://doi.org/10.1216/rmj.2020.50.1115	NOUN
ap-6836	351	4	ľ	ľ	NUM
ap-6836	351	5	.	.	PUNCT
ap-6836	352	1	dvořáková	dvořáková	PROPN
ap-6836	352	2	,	,	PUNCT
ap-6836	352	3	s.	s.	PROPN
ap-6836	352	4	kruml	kruml	PROPN
ap-6836	352	5	,	,	PUNCT
ap-6836	352	6	d.	d.	PROPN
ap-6836	352	7	ryzák	ryzák	VERB
ap-6836	352	8	acta	acta	PROPN
ap-6836	352	9	polytechnica	polytechnica	PROPN
ap-6836	353	1	[	[	X
ap-6836	353	2	4	4	X
ap-6836	353	3	]	]	X
ap-6836	353	4	g.	g.	PROPN
ap-6836	353	5	j.	j.	PROPN
ap-6836	353	6	simmons	simmons	PROPN
ap-6836	353	7	.	.	PUNCT
ap-6836	354	1	on	on	ADP
ap-6836	354	2	palindromic	palindromic	ADJ
ap-6836	354	3	squares	square	NOUN
ap-6836	354	4	of	of	ADP
ap-6836	354	5	non	non	ADJ
ap-6836	354	6	-	-	ADJ
ap-6836	354	7	palindromic	palindromic	ADJ
ap-6836	354	8	numbers	number	NOUN
ap-6836	354	9	.	.	PUNCT
ap-6836	355	1	j	j	PROPN
ap-6836	355	2	recreational	recreational	ADJ
ap-6836	355	3	math	math	PROPN
ap-6836	355	4	5(1):11–19	5(1):11–19	NUM
ap-6836	355	5	,	,	PUNCT
ap-6836	355	6	1972	1972	NUM
ap-6836	355	7	.	.	PUNCT
ap-6836	356	1	[	[	X
ap-6836	356	2	5	5	X
ap-6836	356	3	]	]	X
ap-6836	356	4	g.	g.	PROPN
ap-6836	356	5	j.	j.	PROPN
ap-6836	356	6	simmons	simmons	PROPN
ap-6836	356	7	.	.	PUNCT
ap-6836	357	1	palindromic	palindromic	ADJ
ap-6836	357	2	powers	power	NOUN
ap-6836	357	3	.	.	PUNCT
ap-6836	358	1	j	j	PROPN
ap-6836	358	2	recreational	recreational	ADJ
ap-6836	358	3	math	math	NOUN
ap-6836	358	4	3:93–98	3:93–98	NUM
ap-6836	358	5	,	,	PUNCT
ap-6836	358	6	1970	1970	NUM
ap-6836	358	7	.	.	PUNCT
ap-6836	359	1	[	[	X
ap-6836	359	2	6	6	NUM
ap-6836	359	3	]	]	PUNCT
ap-6836	359	4	w.	w.	PROPN
ap-6836	359	5	d.	d.	PROPN
ap-6836	359	6	banks	banks	PROPN
ap-6836	359	7	,	,	PUNCT
ap-6836	359	8	d.	d.	PROPN
ap-6836	359	9	n.	n.	PROPN
ap-6836	359	10	hart	hart	PROPN
ap-6836	359	11	,	,	PUNCT
ap-6836	359	12	m.	m.	NOUN
ap-6836	359	13	sakata	sakata	PROPN
ap-6836	359	14	.	.	PUNCT
ap-6836	360	1	almost	almost	ADV
ap-6836	360	2	all	all	DET
ap-6836	360	3	palindromes	palindrome	NOUN
ap-6836	360	4	are	be	AUX
ap-6836	360	5	composite	composite	ADJ
ap-6836	360	6	.	.	PUNCT
ap-6836	361	1	math	math	NOUN
ap-6836	361	2	res	re	NOUN
ap-6836	361	3	lett	lett	PROPN
ap-6836	361	4	11(5	11(5	PROPN
ap-6836	361	5	-	-	SYM
ap-6836	361	6	6):853–868	6):853–868	NUM
ap-6836	361	7	,	,	PUNCT
ap-6836	361	8	2004	2004	NUM
ap-6836	361	9	.	.	PUNCT
ap-6836	362	1	https://doi.org/10.4310/mrl.2004.v11.n6.a10	https://doi.org/10.4310/mrl.2004.v11.n6.a10	X
ap-6836	362	2	.	.	PUNCT
ap-6836	363	1	[	[	X
ap-6836	363	2	7	7	X
ap-6836	363	3	]	]	X
ap-6836	363	4	j.	j.	PROPN
ap-6836	363	5	cilleruelo	cilleruelo	PROPN
ap-6836	363	6	,	,	PUNCT
ap-6836	363	7	f.	f.	PROPN
ap-6836	363	8	luca	luca	PROPN
ap-6836	363	9	,	,	PUNCT
ap-6836	363	10	l.	l.	PROPN
ap-6836	363	11	baxter	baxter	PROPN
ap-6836	363	12	.	.	PUNCT
ap-6836	364	1	every	every	DET
ap-6836	364	2	positive	positive	ADJ
ap-6836	364	3	integer	integer	NOUN
ap-6836	364	4	is	be	AUX
ap-6836	364	5	a	a	DET
ap-6836	364	6	sum	sum	NOUN
ap-6836	364	7	of	of	ADP
ap-6836	364	8	three	three	NUM
ap-6836	364	9	palindromes	palindrome	NOUN
ap-6836	364	10	.	.	PUNCT
ap-6836	365	1	math	math	NOUN
ap-6836	365	2	comp	comp	PROPN
ap-6836	365	3	87(314):3023	87(314):3023	PROPN
ap-6836	365	4	–	–	PUNCT
ap-6836	365	5	3055	3055	NUM
ap-6836	365	6	,	,	PUNCT
ap-6836	365	7	2018	2018	NUM
ap-6836	365	8	.	.	PUNCT
ap-6836	366	1	https://doi.org/10.1090/mcom/3221	https://doi.org/10.1090/mcom/3221	PROPN
ap-6836	366	2	.	.	PUNCT
ap-6836	367	1	[	[	X
ap-6836	367	2	8	8	NUM
ap-6836	367	3	]	]	PUNCT
ap-6836	367	4	a.	a.	NOUN
ap-6836	367	5	rajasekaran	rajasekaran	NOUN
ap-6836	367	6	,	,	PUNCT
ap-6836	367	7	j.	j.	PROPN
ap-6836	367	8	shallit	shallit	PROPN
ap-6836	367	9	,	,	PUNCT
ap-6836	367	10	t.	t.	PROPN
ap-6836	367	11	smith	smith	PROPN
ap-6836	367	12	.	.	PUNCT
ap-6836	368	1	additive	additive	ADJ
ap-6836	368	2	number	number	NOUN
ap-6836	368	3	theory	theory	NOUN
ap-6836	368	4	via	via	ADP
ap-6836	368	5	automata	automata	PROPN
ap-6836	368	6	theory	theory	NOUN
ap-6836	368	7	.	.	PUNCT
ap-6836	369	1	theory	theory	NOUN
ap-6836	369	2	comput	comput	PROPN
ap-6836	369	3	syst	syst	PROPN
ap-6836	369	4	64(3):542–567	64(3):542–567	PROPN
ap-6836	369	5	,	,	PUNCT
ap-6836	369	6	2020	2020	NUM
ap-6836	369	7	.	.	PUNCT
ap-6836	370	1	https://doi.org/10.1007/s00224-019-09929-9	https://doi.org/10.1007/s00224-019-09929-9	NUM
ap-6836	370	2	.	.	PUNCT
ap-6836	371	1	[	[	X
ap-6836	371	2	9	9	NUM
ap-6836	371	3	]	]	PUNCT
ap-6836	371	4	s.	s.	PROPN
ap-6836	371	5	kruml	kruml	PROPN
ap-6836	371	6	.	.	PUNCT
ap-6836	372	1	antipalindromic	antipalindromic	ADJ
ap-6836	372	2	numbers	number	NOUN
ap-6836	372	3	(	(	PUNCT
ap-6836	372	4	application	application	NOUN
ap-6836	372	5	)	)	PUNCT
ap-6836	372	6	.	.	PUNCT
ap-6836	373	1	[	[	X
ap-6836	373	2	2020	2020	NUM
ap-6836	373	3	-	-	SYM
ap-6836	373	4	08	08	NUM
ap-6836	373	5	-	-	SYM
ap-6836	373	6	10	10	NUM
ap-6836	373	7	]	]	PUNCT
ap-6836	373	8	,	,	PUNCT
ap-6836	373	9	https	https	NOUN
ap-6836	373	10	:	:	PUNCT
ap-6836	373	11	//github.com	//github.com	X
ap-6836	373	12	/	/	SYM
ap-6836	373	13	kruml3	kruml3	PROPN
ap-6836	373	14	/	/	SYM
ap-6836	373	15	antipalindromic	antipalindromic	NOUN
ap-6836	373	16	-	-	PUNCT
ap-6836	373	17	numbers/.	numbers/.	NOUN
ap-6836	374	1	[	[	X
ap-6836	374	2	10	10	NUM
ap-6836	374	3	]	]	X
ap-6836	374	4	j.	j.	PROPN
ap-6836	374	5	cilleruelo	cilleruelo	PROPN
ap-6836	374	6	,	,	PUNCT
ap-6836	374	7	f.	f.	PROPN
ap-6836	374	8	luca	luca	PROPN
ap-6836	374	9	,	,	PUNCT
ap-6836	374	10	i.	i.	PROPN
ap-6836	374	11	e.	e.	PROPN
ap-6836	374	12	shparlinski	shparlinski	PROPN
ap-6836	374	13	.	.	PUNCT
ap-6836	375	1	power	power	NOUN
ap-6836	375	2	values	value	NOUN
ap-6836	375	3	of	of	ADP
ap-6836	375	4	palindromes	palindrome	NOUN
ap-6836	375	5	.	.	PUNCT
ap-6836	376	1	j	j	PROPN
ap-6836	376	2	comb	comb	NOUN
ap-6836	376	3	number	number	NOUN
ap-6836	376	4	theory	theory	NOUN
ap-6836	376	5	1(2):101–107	1(2):101–107	NUM
ap-6836	376	6	,	,	PUNCT
ap-6836	376	7	2009	2009	NUM
ap-6836	376	8	.	.	PUNCT
ap-6836	377	1	[	[	X
ap-6836	377	2	11	11	NUM
ap-6836	377	3	]	]	PUNCT
ap-6836	377	4	b.	b.	PROPN
ap-6836	377	5	bašić	bašić	PROPN
ap-6836	377	6	.	.	PUNCT
ap-6836	378	1	on	on	ADP
ap-6836	378	2	d	d	ADJ
ap-6836	378	3	-	-	PUNCT
ap-6836	378	4	digit	digit	NOUN
ap-6836	378	5	palindromes	palindrome	NOUN
ap-6836	378	6	in	in	ADP
ap-6836	378	7	different	different	ADJ
ap-6836	378	8	bases	basis	NOUN
ap-6836	378	9	:	:	PUNCT
ap-6836	378	10	the	the	DET
ap-6836	378	11	number	number	NOUN
ap-6836	378	12	of	of	ADP
ap-6836	378	13	bases	basis	NOUN
ap-6836	378	14	is	be	AUX
ap-6836	378	15	unbounded	unbounded	ADJ
ap-6836	378	16	.	.	PUNCT
ap-6836	379	1	int	int	NOUN
ap-6836	379	2	j	j	PROPN
ap-6836	379	3	number	number	NOUN
ap-6836	379	4	theory	theory	NOUN
ap-6836	379	5	8(6):1387–1390	8(6):1387–1390	PROPN
ap-6836	379	6	,	,	PUNCT
ap-6836	379	7	2012	2012	NUM
ap-6836	379	8	.	.	PUNCT
ap-6836	380	1	https://doi.org/10.1142/s1793042112500819	https://doi.org/10.1142/s1793042112500819	X
ap-6836	380	2	.	.	PUNCT
ap-6836	381	1	[	[	X
ap-6836	381	2	12	12	NUM
ap-6836	381	3	]	]	PUNCT
ap-6836	381	4	b.	b.	PROPN
ap-6836	381	5	bašić	bašić	PROPN
ap-6836	381	6	.	.	PUNCT
ap-6836	382	1	on	on	ADP
ap-6836	382	2	“	"	PUNCT
ap-6836	382	3	very	very	ADV
ap-6836	382	4	palindromic	palindromic	ADJ
ap-6836	382	5	”	"	PUNCT
ap-6836	382	6	sequences	sequence	NOUN
ap-6836	382	7	.	.	PUNCT
ap-6836	383	1	j	j	PROPN
ap-6836	383	2	korean	korean	PROPN
ap-6836	383	3	math	math	PROPN
ap-6836	383	4	soc	soc	PROPN
ap-6836	383	5	52(4):765–780	52(4):765–780	PROPN
ap-6836	383	6	,	,	PUNCT
ap-6836	383	7	2015	2015	NUM
ap-6836	383	8	.	.	PUNCT
ap-6836	384	1	https://doi.org/10.4134/jkms.2015.52.4.765	https://doi.org/10.4134/jkms.2015.52.4.765	PROPN
ap-6836	384	2	.	.	PUNCT
ap-6836	385	1	[	[	X
ap-6836	385	2	13	13	NUM
ap-6836	385	3	]	]	PUNCT
ap-6836	385	4	a.	a.	NOUN
ap-6836	385	5	bérczes	bércze	NOUN
ap-6836	385	6	,	,	PUNCT
ap-6836	385	7	v.	v.	PROPN
ap-6836	385	8	ziegler	ziegler	PROPN
ap-6836	385	9	.	.	PUNCT
ap-6836	386	1	on	on	ADP
ap-6836	386	2	simultaneous	simultaneous	ADJ
ap-6836	386	3	palindromes	palindrome	NOUN
ap-6836	386	4	.	.	PUNCT
ap-6836	387	1	j	j	PROPN
ap-6836	387	2	comb	comb	NOUN
ap-6836	387	3	number	number	NOUN
ap-6836	387	4	theory	theory	NOUN
ap-6836	387	5	6(1):37–49	6(1):37–49	NUM
ap-6836	387	6	,	,	PUNCT
ap-6836	387	7	2014	2014	NUM
ap-6836	387	8	.	.	PUNCT
ap-6836	388	1	[	[	X
ap-6836	388	2	14	14	NUM
ap-6836	388	3	]	]	X
ap-6836	388	4	s.	s.	PROPN
ap-6836	388	5	kruml	kruml	PROPN
ap-6836	388	6	.	.	PUNCT
ap-6836	389	1	antipalindromic	antipalindromic	ADJ
ap-6836	389	2	numbers	number	NOUN
ap-6836	389	3	.	.	PUNCT
ap-6836	390	1	bachelor	bachelor	NOUN
ap-6836	390	2	thesis	thesis	NOUN
ap-6836	390	3	,	,	PUNCT
ap-6836	390	4	czech	czech	PROPN
ap-6836	390	5	technical	technical	PROPN
ap-6836	390	6	university	university	PROPN
ap-6836	390	7	in	in	ADP
ap-6836	390	8	prague	prague	PROPN
ap-6836	390	9	,	,	PUNCT
ap-6836	390	10	2020	2020	NUM
ap-6836	390	11	.	.	PUNCT
ap-6836	391	1	available	available	ADJ
ap-6836	391	2	on	on	ADP
ap-6836	391	3	request	request	NOUN
ap-6836	391	4	.	.	PUNCT
ap-6836	392	1	434	434	NUM
ap-6836	392	2	https://doi.org/10.4310/mrl.2004.v11.n6.a10	https://doi.org/10.4310/mrl.2004.v11.n6.a10	PROPN
ap-6836	392	3	https://doi.org/10.1090/mcom/3221	https://doi.org/10.1090/mcom/3221	PROPN
ap-6836	392	4	https://doi.org/10.1007/s00224-019-09929-9	https://doi.org/10.1007/s00224-019-09929-9	NUM
ap-6836	392	5	https://github.com/kruml3/antipalindromic-numbers/	https://github.com/kruml3/antipalindromic-numbers/	ADJ
ap-6836	392	6	https://github.com/kruml3/antipalindromic-numbers/	https://github.com/kruml3/antipalindromic-numbers/	ADJ
ap-6836	392	7	https://doi.org/10.1142/s1793042112500819	https://doi.org/10.1142/s1793042112500819	NUM
ap-6836	392	8	https://doi.org/10.4134/jkms.2015.52.4.765	https://doi.org/10.4134/jkms.2015.52.4.765	PROPN
ap-6836	392	9	acta	acta	PROPN
ap-6836	392	10	polytechnica	polytechnica	PROPN
ap-6836	392	11	61(3):428–434	61(3):428–434	PROPN
ap-6836	392	12	,	,	PUNCT
ap-6836	392	13	2021	2021	NUM
ap-6836	392	14	1	1	NUM
ap-6836	392	15	introduction	introduction	NOUN
ap-6836	392	16	2	2	NUM
ap-6836	392	17	definition	definition	NOUN
ap-6836	392	18	and	and	CCONJ
ap-6836	392	19	basic	basic	ADJ
ap-6836	392	20	properties	property	NOUN
ap-6836	392	21	3	3	NUM
ap-6836	392	22	divisibility	divisibility	NOUN
ap-6836	392	23	and	and	CCONJ
ap-6836	392	24	antipalindromic	antipalindromic	ADJ
ap-6836	392	25	primes	prime	NOUN
ap-6836	392	26	4	4	NUM
ap-6836	392	27	squares	square	NOUN
ap-6836	392	28	and	and	CCONJ
ap-6836	392	29	other	other	ADJ
ap-6836	392	30	powers	power	NOUN
ap-6836	392	31	as	as	ADP
ap-6836	392	32	antipalindromes	antipalindrome	NOUN
ap-6836	392	33	5	5	NUM
ap-6836	392	34	multi	multi	ADJ
ap-6836	392	35	-	-	ADJ
ap-6836	392	36	base	base	ADJ
ap-6836	392	37	antipalindromic	antipalindromic	ADJ
ap-6836	392	38	numbers	number	NOUN
ap-6836	392	39	6	6	NUM
ap-6836	392	40	conclusion	conclusion	NOUN
ap-6836	392	41	and	and	CCONJ
ap-6836	392	42	open	open	ADJ
ap-6836	392	43	problems	problem	NOUN
ap-6836	392	44	acknowledgements	acknowledgement	NOUN
ap-6836	392	45	references	reference	NOUN