id	sid	tid	token	lemma	pos
american_scientific_journal-7485	1	1	91	91	NUM
american_scientific_journal-7485	1	2	american	american	ADJ
american_scientific_journal-7485	1	3	academic	academic	ADJ
american_scientific_journal-7485	1	4	scientific	scientific	ADJ
american_scientific_journal-7485	1	5	research	research	NOUN
american_scientific_journal-7485	1	6	journal	journal	NOUN
american_scientific_journal-7485	1	7	for	for	ADP
american_scientific_journal-7485	1	8	engineering	engineering	NOUN
american_scientific_journal-7485	1	9	,	,	PUNCT
american_scientific_journal-7485	1	10	technology	technology	NOUN
american_scientific_journal-7485	1	11	,	,	PUNCT
american_scientific_journal-7485	1	12	and	and	CCONJ
american_scientific_journal-7485	1	13	sciences	sciences	PROPN
american_scientific_journal-7485	1	14	issn	issn	PROPN
american_scientific_journal-7485	1	15	(	(	PUNCT
american_scientific_journal-7485	1	16	print	print	NOUN
american_scientific_journal-7485	1	17	)	)	PUNCT
american_scientific_journal-7485	1	18	2313	2313	NUM
american_scientific_journal-7485	1	19	-	-	SYM
american_scientific_journal-7485	1	20	4410	4410	NUM
american_scientific_journal-7485	1	21	,	,	PUNCT
american_scientific_journal-7485	1	22	issn	issn	PROPN
american_scientific_journal-7485	1	23	(	(	PUNCT
american_scientific_journal-7485	1	24	online	online	ADJ
american_scientific_journal-7485	1	25	)	)	PUNCT
american_scientific_journal-7485	1	26	2313	2313	NUM
american_scientific_journal-7485	1	27	-	-	SYM
american_scientific_journal-7485	1	28	4402	4402	NUM
american_scientific_journal-7485	1	29	http://asrjetsjournal.org/	http://asrjetsjournal.org/	NOUN
american_scientific_journal-7485	1	30	a	a	DET
american_scientific_journal-7485	1	31	new	new	ADJ
american_scientific_journal-7485	1	32	way	way	NOUN
american_scientific_journal-7485	1	33	of	of	ADP
american_scientific_journal-7485	1	34	looking	look	VERB
american_scientific_journal-7485	1	35	at	at	ADP
american_scientific_journal-7485	1	36	the	the	DET
american_scientific_journal-7485	1	37	collatz	collatz	NOUN
american_scientific_journal-7485	1	38	conjecture	conjecture	NOUN
american_scientific_journal-7485	1	39	lourens	louren	VERB
american_scientific_journal-7485	1	40	nicolaas	nicolaas	ADJ
american_scientific_journal-7485	1	41	jacobus	jacobus	PROPN
american_scientific_journal-7485	1	42	engelbrecht	engelbrecht	PROPN
american_scientific_journal-7485	1	43	*	*	PUNCT
american_scientific_journal-7485	1	44	independent	independent	ADJ
american_scientific_journal-7485	1	45	researcher	researcher	NOUN
american_scientific_journal-7485	1	46	,	,	PUNCT
american_scientific_journal-7485	1	47	33	33	NUM
american_scientific_journal-7485	1	48	william	william	PROPN
american_scientific_journal-7485	1	49	road	road	PROPN
american_scientific_journal-7485	1	50	,	,	PUNCT
american_scientific_journal-7485	1	51	pringle	pringle	PROPN
american_scientific_journal-7485	1	52	bay	bay	PROPN
american_scientific_journal-7485	1	53	7196	7196	NUM
american_scientific_journal-7485	1	54	,	,	PUNCT
american_scientific_journal-7485	1	55	south	south	PROPN
american_scientific_journal-7485	1	56	africa	africa	PROPN
american_scientific_journal-7485	1	57	email	email	NOUN
american_scientific_journal-7485	1	58	:	:	PUNCT
american_scientific_journal-7485	1	59	engelbrechtlourie@gmail.com	engelbrechtlourie@gmail.com	PROPN
american_scientific_journal-7485	2	1	abstract	abstract	ADJ
american_scientific_journal-7485	2	2	the	the	DET
american_scientific_journal-7485	2	3	collatz	collatz	NOUN
american_scientific_journal-7485	2	4	conjecture	conjecture	NOUN
american_scientific_journal-7485	2	5	is	be	AUX
american_scientific_journal-7485	2	6	named	name	VERB
american_scientific_journal-7485	2	7	after	after	ADP
american_scientific_journal-7485	2	8	a	a	DET
american_scientific_journal-7485	2	9	mathematician	mathematician	ADJ
american_scientific_journal-7485	2	10	lothar	lothar	PROPN
american_scientific_journal-7485	2	11	collatz	collatz	NOUN
american_scientific_journal-7485	2	12	who	who	PRON
american_scientific_journal-7485	2	13	introduced	introduce	VERB
american_scientific_journal-7485	2	14	the	the	DET
american_scientific_journal-7485	2	15	conjecture	conjecture	NOUN
american_scientific_journal-7485	2	16	in	in	ADP
american_scientific_journal-7485	2	17	1937	1937	NUM
american_scientific_journal-7485	2	18	.	.	PUNCT
american_scientific_journal-7485	3	1	the	the	DET
american_scientific_journal-7485	3	2	collatz	collatz	PROPN
american_scientific_journal-7485	3	3	conjecture	conjecture	NOUN
american_scientific_journal-7485	3	4	which	which	PRON
american_scientific_journal-7485	3	5	remains	remain	VERB
american_scientific_journal-7485	3	6	an	an	DET
american_scientific_journal-7485	3	7	unsolved	unsolved	ADJ
american_scientific_journal-7485	3	8	problem	problem	NOUN
american_scientific_journal-7485	3	9	in	in	ADP
american_scientific_journal-7485	3	10	mathematics	mathematics	PROPN
american_scientific_journal-7485	3	11	today	today	NOUN
american_scientific_journal-7485	3	12	,	,	PUNCT
american_scientific_journal-7485	3	13	also	also	ADV
american_scientific_journal-7485	3	14	known	know	VERB
american_scientific_journal-7485	3	15	as	as	ADP
american_scientific_journal-7485	3	16	the	the	DET
american_scientific_journal-7485	3	17	“	"	PUNCT
american_scientific_journal-7485	3	18	3n	3n	NUM
american_scientific_journal-7485	3	19	+	+	SYM
american_scientific_journal-7485	3	20	1	1	NUM
american_scientific_journal-7485	3	21	conjecture	conjecture	NOUN
american_scientific_journal-7485	3	22	”	"	PUNCT
american_scientific_journal-7485	3	23	,	,	PUNCT
american_scientific_journal-7485	3	24	explains	explain	VERB
american_scientific_journal-7485	3	25	about	about	ADP
american_scientific_journal-7485	3	26	a	a	DET
american_scientific_journal-7485	3	27	sequence	sequence	NOUN
american_scientific_journal-7485	3	28	defined	define	VERB
american_scientific_journal-7485	3	29	as	as	SCONJ
american_scientific_journal-7485	3	30	follows	follow	VERB
american_scientific_journal-7485	3	31	:	:	PUNCT
american_scientific_journal-7485	3	32	start	start	VERB
american_scientific_journal-7485	3	33	with	with	ADP
american_scientific_journal-7485	3	34	any	any	DET
american_scientific_journal-7485	3	35	positive	positive	ADJ
american_scientific_journal-7485	3	36	integer	integer	NOUN
american_scientific_journal-7485	3	37	,	,	PUNCT
american_scientific_journal-7485	3	38	the	the	DET
american_scientific_journal-7485	3	39	starting	start	VERB
american_scientific_journal-7485	3	40	integer	integer	NOUN
american_scientific_journal-7485	3	41	can	can	AUX
american_scientific_journal-7485	3	42	be	be	AUX
american_scientific_journal-7485	3	43	an	an	DET
american_scientific_journal-7485	3	44	even	even	ADJ
american_scientific_journal-7485	3	45	number	number	NOUN
american_scientific_journal-7485	3	46	or	or	CCONJ
american_scientific_journal-7485	3	47	an	an	DET
american_scientific_journal-7485	3	48	odd	odd	ADJ
american_scientific_journal-7485	3	49	number	number	NOUN
american_scientific_journal-7485	3	50	.	.	PUNCT
american_scientific_journal-7485	4	1	consider	consider	VERB
american_scientific_journal-7485	4	2	a	a	DET
american_scientific_journal-7485	4	3	number	number	NOUN
american_scientific_journal-7485	4	4	n	n	CCONJ
american_scientific_journal-7485	4	5	,	,	PUNCT
american_scientific_journal-7485	4	6	if	if	SCONJ
american_scientific_journal-7485	4	7	the	the	DET
american_scientific_journal-7485	4	8	number	number	NOUN
american_scientific_journal-7485	4	9	n	n	PART
american_scientific_journal-7485	4	10	is	be	AUX
american_scientific_journal-7485	4	11	even	even	ADV
american_scientific_journal-7485	4	12	,	,	PUNCT
american_scientific_journal-7485	4	13	divide	divide	VERB
american_scientific_journal-7485	4	14	it	it	PRON
american_scientific_journal-7485	4	15	by	by	ADP
american_scientific_journal-7485	4	16	2	2	NUM
american_scientific_journal-7485	4	17	.	.	PUNCT
american_scientific_journal-7485	5	1	if	if	SCONJ
american_scientific_journal-7485	5	2	the	the	DET
american_scientific_journal-7485	5	3	number	number	NOUN
american_scientific_journal-7485	5	4	n	n	PART
american_scientific_journal-7485	5	5	is	be	AUX
american_scientific_journal-7485	5	6	odd	odd	ADJ
american_scientific_journal-7485	5	7	,	,	PUNCT
american_scientific_journal-7485	5	8	triple	triple	ADJ
american_scientific_journal-7485	5	9	it	it	PRON
american_scientific_journal-7485	5	10	and	and	CCONJ
american_scientific_journal-7485	5	11	add	add	VERB
american_scientific_journal-7485	5	12	one	one	NUM
american_scientific_journal-7485	5	13	.	.	PUNCT
american_scientific_journal-7485	6	1	further	far	ADV
american_scientific_journal-7485	6	2	,	,	PUNCT
american_scientific_journal-7485	6	3	it	it	PRON
american_scientific_journal-7485	6	4	states	state	VERB
american_scientific_journal-7485	6	5	that	that	SCONJ
american_scientific_journal-7485	6	6	regardless	regardless	ADV
american_scientific_journal-7485	6	7	of	of	ADP
american_scientific_journal-7485	6	8	the	the	DET
american_scientific_journal-7485	6	9	choice	choice	NOUN
american_scientific_journal-7485	6	10	of	of	ADP
american_scientific_journal-7485	6	11	n	n	CCONJ
american_scientific_journal-7485	6	12	,	,	PUNCT
american_scientific_journal-7485	6	13	after	after	ADP
american_scientific_journal-7485	6	14	some	some	DET
american_scientific_journal-7485	6	15	iterations	iteration	NOUN
american_scientific_journal-7485	6	16	of	of	ADP
american_scientific_journal-7485	6	17	the	the	DET
american_scientific_journal-7485	6	18	conjecture	conjecture	NOUN
american_scientific_journal-7485	6	19	,	,	PUNCT
american_scientific_journal-7485	6	20	the	the	DET
american_scientific_journal-7485	6	21	number	number	NOUN
american_scientific_journal-7485	6	22	no	no	ADV
american_scientific_journal-7485	6	23	matter	matter	ADV
american_scientific_journal-7485	6	24	what	what	DET
american_scientific_journal-7485	6	25	value	value	NOUN
american_scientific_journal-7485	6	26	of	of	ADP
american_scientific_journal-7485	6	27	a	a	DET
american_scientific_journal-7485	6	28	positive	positive	ADJ
american_scientific_journal-7485	6	29	n	n	NOUN
american_scientific_journal-7485	6	30	is	be	AUX
american_scientific_journal-7485	6	31	chosen	choose	VERB
american_scientific_journal-7485	6	32	,	,	PUNCT
american_scientific_journal-7485	6	33	the	the	DET
american_scientific_journal-7485	6	34	sequence	sequence	NOUN
american_scientific_journal-7485	6	35	from	from	ADP
american_scientific_journal-7485	6	36	the	the	DET
american_scientific_journal-7485	6	37	number	number	NOUN
american_scientific_journal-7485	6	38	chosen	choose	VERB
american_scientific_journal-7485	6	39	,	,	PUNCT
american_scientific_journal-7485	6	40	projecting	project	VERB
american_scientific_journal-7485	6	41	between	between	ADP
american_scientific_journal-7485	6	42	lower	low	ADJ
american_scientific_journal-7485	6	43	and	and	CCONJ
american_scientific_journal-7485	6	44	peak	peak	NOUN
american_scientific_journal-7485	6	45	values	value	NOUN
american_scientific_journal-7485	6	46	will	will	AUX
american_scientific_journal-7485	6	47	eventually	eventually	ADV
american_scientific_journal-7485	6	48	attains	attain	VERB
american_scientific_journal-7485	6	49	the	the	DET
american_scientific_journal-7485	6	50	value	value	NOUN
american_scientific_journal-7485	6	51	of	of	ADP
american_scientific_journal-7485	6	52	1	1	NUM
american_scientific_journal-7485	6	53	.	.	PUNCT
american_scientific_journal-7485	7	1	once	once	ADV
american_scientific_journal-7485	7	2	reaching	reach	VERB
american_scientific_journal-7485	7	3	the	the	DET
american_scientific_journal-7485	7	4	value	value	NOUN
american_scientific_journal-7485	7	5	of	of	ADP
american_scientific_journal-7485	7	6	1	1	NUM
american_scientific_journal-7485	7	7	it	it	PRON
american_scientific_journal-7485	7	8	will	will	AUX
american_scientific_journal-7485	7	9	cycle	cycle	VERB
american_scientific_journal-7485	7	10	through	through	ADP
american_scientific_journal-7485	7	11	the	the	DET
american_scientific_journal-7485	7	12	values	value	NOUN
american_scientific_journal-7485	7	13	1	1	NUM
american_scientific_journal-7485	7	14	,	,	PUNCT
american_scientific_journal-7485	7	15	4	4	NUM
american_scientific_journal-7485	7	16	,	,	PUNCT
american_scientific_journal-7485	7	17	2	2	NUM
american_scientific_journal-7485	7	18	indefinitely	indefinitely	ADV
american_scientific_journal-7485	7	19	.	.	PUNCT
american_scientific_journal-7485	8	1	the	the	DET
american_scientific_journal-7485	8	2	projections	projection	NOUN
american_scientific_journal-7485	8	3	of	of	ADP
american_scientific_journal-7485	8	4	numbers	number	NOUN
american_scientific_journal-7485	8	5	involved	involve	VERB
american_scientific_journal-7485	8	6	in	in	ADP
american_scientific_journal-7485	8	7	this	this	DET
american_scientific_journal-7485	8	8	conjecture	conjecture	NOUN
american_scientific_journal-7485	8	9	is	be	AUX
american_scientific_journal-7485	8	10	sometimes	sometimes	ADV
american_scientific_journal-7485	8	11	referred	refer	VERB
american_scientific_journal-7485	8	12	to	to	ADP
american_scientific_journal-7485	8	13	as	as	ADP
american_scientific_journal-7485	8	14	“	"	PUNCT
american_scientific_journal-7485	8	15	hailstone	hailstone	NOUN
american_scientific_journal-7485	8	16	numbers	number	NOUN
american_scientific_journal-7485	8	17	”	"	PUNCT
american_scientific_journal-7485	8	18	[	[	X
american_scientific_journal-7485	8	19	1	1	NUM
american_scientific_journal-7485	8	20	]	]	PUNCT
american_scientific_journal-7485	8	21	because	because	SCONJ
american_scientific_journal-7485	8	22	of	of	ADP
american_scientific_journal-7485	8	23	the	the	DET
american_scientific_journal-7485	8	24	different	different	ADJ
american_scientific_journal-7485	8	25	projections	projection	NOUN
american_scientific_journal-7485	8	26	of	of	ADP
american_scientific_journal-7485	8	27	each	each	DET
american_scientific_journal-7485	8	28	number	number	NOUN
american_scientific_journal-7485	8	29	in	in	ADP
american_scientific_journal-7485	8	30	multiple	multiple	ADJ
american_scientific_journal-7485	8	31	descents	descent	NOUN
american_scientific_journal-7485	8	32	and	and	CCONJ
american_scientific_journal-7485	8	33	ascents	ascent	NOUN
american_scientific_journal-7485	8	34	before	before	ADP
american_scientific_journal-7485	8	35	reaching	reach	VERB
american_scientific_journal-7485	8	36	the	the	DET
american_scientific_journal-7485	8	37	number	number	NOUN
american_scientific_journal-7485	8	38	1	1	NUM
american_scientific_journal-7485	8	39	.	.	PUNCT
american_scientific_journal-7485	9	1	i	i	PRON
american_scientific_journal-7485	9	2	believe	believe	VERB
american_scientific_journal-7485	9	3	that	that	SCONJ
american_scientific_journal-7485	9	4	the	the	DET
american_scientific_journal-7485	9	5	ideas	idea	NOUN
american_scientific_journal-7485	9	6	here	here	ADV
american_scientific_journal-7485	9	7	represent	represent	VERB
american_scientific_journal-7485	9	8	an	an	DET
american_scientific_journal-7485	9	9	interesting	interesting	ADJ
american_scientific_journal-7485	9	10	new	new	ADJ
american_scientific_journal-7485	9	11	approach	approach	NOUN
american_scientific_journal-7485	9	12	towards	towards	ADP
american_scientific_journal-7485	9	13	understanding	understand	VERB
american_scientific_journal-7485	9	14	the	the	DET
american_scientific_journal-7485	9	15	collatz	collatz	NOUN
american_scientific_journal-7485	9	16	conjecture	conjecture	VERB
american_scientific_journal-7485	9	17	’s	’s	PART
american_scientific_journal-7485	9	18	sequences	sequence	NOUN
american_scientific_journal-7485	9	19	of	of	ADP
american_scientific_journal-7485	9	20	numbers	number	NOUN
american_scientific_journal-7485	9	21	,	,	PUNCT
american_scientific_journal-7485	9	22	especially	especially	ADV
american_scientific_journal-7485	9	23	the	the	DET
american_scientific_journal-7485	9	24	effect	effect	NOUN
american_scientific_journal-7485	9	25	of	of	ADP
american_scientific_journal-7485	9	26	the	the	DET
american_scientific_journal-7485	9	27	properties	property	NOUN
american_scientific_journal-7485	9	28	of	of	ADP
american_scientific_journal-7485	9	29	even	even	ADV
american_scientific_journal-7485	9	30	numbers	number	NOUN
american_scientific_journal-7485	9	31	divisible	divisible	ADJ
american_scientific_journal-7485	9	32	by	by	ADP
american_scientific_journal-7485	9	33	6	6	NUM
american_scientific_journal-7485	9	34	,	,	PUNCT
american_scientific_journal-7485	9	35	odd	odd	ADJ
american_scientific_journal-7485	9	36	numbers	number	NOUN
american_scientific_journal-7485	9	37	divisible	divisible	ADJ
american_scientific_journal-7485	9	38	by	by	ADP
american_scientific_journal-7485	9	39	3	3	NUM
american_scientific_journal-7485	9	40	,	,	PUNCT
american_scientific_journal-7485	9	41	prime	prime	ADJ
american_scientific_journal-7485	9	42	numbers	number	NOUN
american_scientific_journal-7485	9	43	and	and	CCONJ
american_scientific_journal-7485	9	44	a	a	DET
american_scientific_journal-7485	9	45	set	set	NOUN
american_scientific_journal-7485	9	46	pattern	pattern	NOUN
american_scientific_journal-7485	9	47	in	in	ADP
american_scientific_journal-7485	9	48	the	the	DET
american_scientific_journal-7485	9	49	projections	projection	NOUN
american_scientific_journal-7485	9	50	in	in	ADP
american_scientific_journal-7485	9	51	a	a	DET
american_scientific_journal-7485	9	52	certain	certain	ADJ
american_scientific_journal-7485	9	53	arrangement	arrangement	NOUN
american_scientific_journal-7485	9	54	.	.	PUNCT
american_scientific_journal-7485	10	1	following	follow	VERB
american_scientific_journal-7485	10	2	the	the	DET
american_scientific_journal-7485	10	3	theme	theme	NOUN
american_scientific_journal-7485	10	4	,	,	PUNCT
american_scientific_journal-7485	10	5	here	here	ADV
american_scientific_journal-7485	10	6	in	in	ADP
american_scientific_journal-7485	10	7	this	this	DET
american_scientific_journal-7485	10	8	article	article	NOUN
american_scientific_journal-7485	10	9	a	a	DET
american_scientific_journal-7485	10	10	defined	define	VERB
american_scientific_journal-7485	10	11	pattern	pattern	NOUN
american_scientific_journal-7485	10	12	in	in	ADP
american_scientific_journal-7485	10	13	the	the	DET
american_scientific_journal-7485	10	14	sequence	sequence	NOUN
american_scientific_journal-7485	10	15	of	of	ADP
american_scientific_journal-7485	10	16	the	the	DET
american_scientific_journal-7485	10	17	projections	projection	NOUN
american_scientific_journal-7485	10	18	which	which	PRON
american_scientific_journal-7485	10	19	eluded	elude	VERB
american_scientific_journal-7485	10	20	mathematicians	mathematician	NOUN
american_scientific_journal-7485	10	21	for	for	ADP
american_scientific_journal-7485	10	22	years	year	NOUN
american_scientific_journal-7485	10	23	are	be	AUX
american_scientific_journal-7485	10	24	discussed	discuss	VERB
american_scientific_journal-7485	10	25	.	.	PUNCT
american_scientific_journal-7485	11	1	this	this	PRON
american_scientific_journal-7485	11	2	had	have	AUX
american_scientific_journal-7485	11	3	also	also	ADV
american_scientific_journal-7485	11	4	been	be	AUX
american_scientific_journal-7485	11	5	computer	computer	NOUN
american_scientific_journal-7485	11	6	tested	test	VERB
american_scientific_journal-7485	11	7	and	and	CCONJ
american_scientific_journal-7485	11	8	verified	verify	VERB
american_scientific_journal-7485	11	9	as	as	ADP
american_scientific_journal-7485	11	10	true	true	ADJ
american_scientific_journal-7485	11	11	to	to	ADP
american_scientific_journal-7485	11	12	2	2	NUM
american_scientific_journal-7485	11	13	68	68	NUM
american_scientific_journal-7485	11	14	in	in	ADP
american_scientific_journal-7485	11	15	2020	2020	NUM
american_scientific_journal-7485	11	16	.	.	PUNCT
american_scientific_journal-7485	12	1	keywords	keyword	NOUN
american_scientific_journal-7485	12	2	:	:	PUNCT
american_scientific_journal-7485	12	3	prime	prime	ADJ
american_scientific_journal-7485	12	4	numbers	number	NOUN
american_scientific_journal-7485	12	5	;	;	PUNCT
american_scientific_journal-7485	12	6	congruence	congruence	NOUN
american_scientific_journal-7485	12	7	;	;	PUNCT
american_scientific_journal-7485	12	8	collatz	collatz	NOUN
american_scientific_journal-7485	12	9	conjecture	conjecture	NOUN
american_scientific_journal-7485	12	10	;	;	PUNCT
american_scientific_journal-7485	12	11	hailstone	hailstone	NOUN
american_scientific_journal-7485	12	12	numbers	number	NOUN
american_scientific_journal-7485	12	13	.	.	PUNCT
american_scientific_journal-7485	13	1	1	1	X
american_scientific_journal-7485	13	2	.	.	X
american_scientific_journal-7485	13	3	introduction	introduction	NOUN
american_scientific_journal-7485	13	4	mathematical	mathematical	ADJ
american_scientific_journal-7485	13	5	theorems	theorem	NOUN
american_scientific_journal-7485	13	6	are	be	AUX
american_scientific_journal-7485	13	7	important	important	ADJ
american_scientific_journal-7485	13	8	building	building	NOUN
american_scientific_journal-7485	13	9	blocks	block	NOUN
american_scientific_journal-7485	13	10	for	for	ADP
american_scientific_journal-7485	13	11	applications	application	NOUN
american_scientific_journal-7485	13	12	in	in	ADP
american_scientific_journal-7485	13	13	mathematics	mathematic	NOUN
american_scientific_journal-7485	13	14	and	and	CCONJ
american_scientific_journal-7485	13	15	computing	computing	NOUN
american_scientific_journal-7485	13	16	.	.	PUNCT
american_scientific_journal-7485	14	1	other	other	ADJ
american_scientific_journal-7485	14	2	uses	use	NOUN
american_scientific_journal-7485	14	3	are	be	AUX
american_scientific_journal-7485	14	4	for	for	ADP
american_scientific_journal-7485	14	5	general	general	ADJ
american_scientific_journal-7485	14	6	research	research	NOUN
american_scientific_journal-7485	14	7	,	,	PUNCT
american_scientific_journal-7485	14	8	cryptography	cryptography	NOUN
american_scientific_journal-7485	14	9	,	,	PUNCT
american_scientific_journal-7485	14	10	encryption	encryption	NOUN
american_scientific_journal-7485	14	11	and	and	CCONJ
american_scientific_journal-7485	14	12	many	many	ADJ
american_scientific_journal-7485	14	13	more	more	ADJ
american_scientific_journal-7485	14	14	applications	application	NOUN
american_scientific_journal-7485	14	15	in	in	ADP
american_scientific_journal-7485	14	16	everyday	everyday	ADJ
american_scientific_journal-7485	14	17	use	use	NOUN
american_scientific_journal-7485	14	18	.	.	PUNCT
american_scientific_journal-7485	15	1	no	no	DET
american_scientific_journal-7485	15	2	consensus	consensus	NOUN
american_scientific_journal-7485	15	3	exist	exist	VERB
american_scientific_journal-7485	15	4	yet	yet	ADV
american_scientific_journal-7485	15	5	for	for	ADP
american_scientific_journal-7485	15	6	the	the	DET
american_scientific_journal-7485	15	7	proof	proof	NOUN
american_scientific_journal-7485	15	8	of	of	ADP
american_scientific_journal-7485	15	9	the	the	DET
american_scientific_journal-7485	15	10	collatz	collatz	NOUN
american_scientific_journal-7485	15	11	conjecture	conjecture	VERB
american_scientific_journal-7485	15	12	.	.	PUNCT
american_scientific_journal-7485	16	1	the	the	DET
american_scientific_journal-7485	16	2	search	search	NOUN
american_scientific_journal-7485	16	3	for	for	ADP
american_scientific_journal-7485	16	4	proof	proof	NOUN
american_scientific_journal-7485	16	5	are	be	AUX
american_scientific_journal-7485	16	6	of	of	ADP
american_scientific_journal-7485	16	7	importance	importance	NOUN
american_scientific_journal-7485	16	8	to	to	ADP
american_scientific_journal-7485	16	9	mathematics	mathematic	NOUN
american_scientific_journal-7485	16	10	as	as	SCONJ
american_scientific_journal-7485	16	11	it	it	PRON
american_scientific_journal-7485	16	12	may	may	AUX
american_scientific_journal-7485	16	13	contribute	contribute	VERB
american_scientific_journal-7485	16	14	to	to	ADP
american_scientific_journal-7485	16	15	a	a	DET
american_scientific_journal-7485	16	16	better	well	ADJ
american_scientific_journal-7485	16	17	understanding	understanding	NOUN
american_scientific_journal-7485	16	18	of	of	ADP
american_scientific_journal-7485	16	19	number	number	NOUN
american_scientific_journal-7485	16	20	theory	theory	NOUN
american_scientific_journal-7485	16	21	,	,	PUNCT
american_scientific_journal-7485	16	22	and	and	CCONJ
american_scientific_journal-7485	16	23	even	even	ADV
american_scientific_journal-7485	16	24	help	help	VERB
american_scientific_journal-7485	16	25	to	to	PART
american_scientific_journal-7485	16	26	solve	solve	VERB
american_scientific_journal-7485	16	27	other	other	ADJ
american_scientific_journal-7485	16	28	known	know	VERB
american_scientific_journal-7485	16	29	problems	problem	NOUN
american_scientific_journal-7485	16	30	and	and	CCONJ
american_scientific_journal-7485	16	31	applications	application	NOUN
american_scientific_journal-7485	16	32	.	.	PUNCT
american_scientific_journal-7485	17	1	-----------------------------------------------------------------------	-----------------------------------------------------------------------	PUNCT
american_scientific_journal-7485	18	1	*	*	PUNCT
american_scientific_journal-7485	18	2	corresponding	correspond	VERB
american_scientific_journal-7485	18	3	author	author	NOUN
american_scientific_journal-7485	18	4	.	.	PUNCT
american_scientific_journal-7485	19	1	http://asrjetsjournal.org/	http://asrjetsjournal.org/	PROPN
american_scientific_journal-7485	19	2	american	american	PROPN
american_scientific_journal-7485	19	3	academic	academic	PROPN
american_scientific_journal-7485	19	4	scientific	scientific	ADJ
american_scientific_journal-7485	19	5	research	research	NOUN
american_scientific_journal-7485	19	6	journal	journal	NOUN
american_scientific_journal-7485	19	7	for	for	ADP
american_scientific_journal-7485	19	8	engineering	engineering	NOUN
american_scientific_journal-7485	19	9	,	,	PUNCT
american_scientific_journal-7485	19	10	technology	technology	NOUN
american_scientific_journal-7485	19	11	,	,	PUNCT
american_scientific_journal-7485	19	12	and	and	CCONJ
american_scientific_journal-7485	19	13	sciences	science	NOUN
american_scientific_journal-7485	19	14	(	(	PUNCT
american_scientific_journal-7485	19	15	asrjets	asrjet	NOUN
american_scientific_journal-7485	19	16	)	)	PUNCT
american_scientific_journal-7485	19	17	(	(	PUNCT
american_scientific_journal-7485	19	18	2022	2022	NUM
american_scientific_journal-7485	19	19	)	)	PUNCT
american_scientific_journal-7485	19	20	volume	volume	NOUN
american_scientific_journal-7485	19	21	88	88	NUM
american_scientific_journal-7485	19	22	,	,	PUNCT
american_scientific_journal-7485	19	23	no	no	DET
american_scientific_journal-7485	19	24	1	1	NUM
american_scientific_journal-7485	19	25	,	,	PUNCT
american_scientific_journal-7485	19	26	pp	pp	ADV
american_scientific_journal-7485	19	27	91	91	NUM
american_scientific_journal-7485	19	28	-	-	SYM
american_scientific_journal-7485	19	29	98	98	NUM
american_scientific_journal-7485	19	30	92	92	NUM
american_scientific_journal-7485	19	31	the	the	DET
american_scientific_journal-7485	19	32	famous	famous	ADJ
american_scientific_journal-7485	19	33	mathematician	mathematician	NOUN
american_scientific_journal-7485	19	34	paul	paul	PROPN
american_scientific_journal-7485	19	35	erdos	erdo	NOUN
american_scientific_journal-7485	19	36	said	say	VERB
american_scientific_journal-7485	19	37	that	that	SCONJ
american_scientific_journal-7485	19	38	“	"	PUNCT
american_scientific_journal-7485	19	39	mathematics	mathematic	NOUN
american_scientific_journal-7485	19	40	may	may	AUX
american_scientific_journal-7485	19	41	not	not	PART
american_scientific_journal-7485	19	42	be	be	AUX
american_scientific_journal-7485	19	43	ready	ready	ADJ
american_scientific_journal-7485	19	44	for	for	ADP
american_scientific_journal-7485	19	45	such	such	ADJ
american_scientific_journal-7485	19	46	problems	problem	NOUN
american_scientific_journal-7485	19	47	”	"	PUNCT
american_scientific_journal-7485	19	48	referring	refer	VERB
american_scientific_journal-7485	19	49	to	to	ADP
american_scientific_journal-7485	19	50	the	the	DET
american_scientific_journal-7485	19	51	collatz	collatz	NOUN
american_scientific_journal-7485	19	52	conjecture	conjecture	VERB
american_scientific_journal-7485	19	53	,	,	PUNCT
american_scientific_journal-7485	19	54	and	and	CCONJ
american_scientific_journal-7485	19	55	jeffrey	jeffrey	PROPN
american_scientific_journal-7485	19	56	lagarias	lagarias	PROPN
american_scientific_journal-7485	19	57	in	in	ADP
american_scientific_journal-7485	19	58	[	[	X
american_scientific_journal-7485	19	59	2	2	NUM
american_scientific_journal-7485	19	60	]	]	PUNCT
american_scientific_journal-7485	19	61	,	,	PUNCT
american_scientific_journal-7485	19	62	another	another	DET
american_scientific_journal-7485	19	63	famous	famous	ADJ
american_scientific_journal-7485	19	64	mathematician	mathematician	NOUN
american_scientific_journal-7485	19	65	stated	state	VERB
american_scientific_journal-7485	19	66	in	in	ADP
american_scientific_journal-7485	19	67	2010	2010	NUM
american_scientific_journal-7485	19	68	,	,	PUNCT
american_scientific_journal-7485	19	69	“	"	PUNCT
american_scientific_journal-7485	19	70	this	this	PRON
american_scientific_journal-7485	19	71	is	be	AUX
american_scientific_journal-7485	19	72	an	an	DET
american_scientific_journal-7485	19	73	extraordinarily	extraordinarily	ADV
american_scientific_journal-7485	19	74	difficult	difficult	ADJ
american_scientific_journal-7485	19	75	problem	problem	NOUN
american_scientific_journal-7485	19	76	,	,	PUNCT
american_scientific_journal-7485	19	77	completely	completely	ADV
american_scientific_journal-7485	19	78	out	out	ADP
american_scientific_journal-7485	19	79	of	of	ADP
american_scientific_journal-7485	19	80	reach	reach	NOUN
american_scientific_journal-7485	19	81	of	of	ADP
american_scientific_journal-7485	19	82	present	present	ADJ
american_scientific_journal-7485	19	83	day	day	NOUN
american_scientific_journal-7485	19	84	mathematics	mathematic	NOUN
american_scientific_journal-7485	19	85	”	"	PUNCT
american_scientific_journal-7485	19	86	.	.	PUNCT
american_scientific_journal-7485	20	1	a	a	DET
american_scientific_journal-7485	20	2	more	more	ADV
american_scientific_journal-7485	20	3	recent	recent	ADJ
american_scientific_journal-7485	20	4	attempt	attempt	NOUN
american_scientific_journal-7485	20	5	to	to	PART
american_scientific_journal-7485	20	6	prove	prove	VERB
american_scientific_journal-7485	20	7	the	the	DET
american_scientific_journal-7485	20	8	conjecture	conjecture	NOUN
american_scientific_journal-7485	20	9	as	as	ADP
american_scientific_journal-7485	20	10	true	true	ADJ
american_scientific_journal-7485	20	11	was	be	AUX
american_scientific_journal-7485	20	12	posted	post	VERB
american_scientific_journal-7485	20	13	in	in	ADP
american_scientific_journal-7485	20	14	2019	2019	NUM
american_scientific_journal-7485	20	15	by	by	ADP
american_scientific_journal-7485	20	16	terrance	terrance	PROPN
american_scientific_journal-7485	20	17	tau	tau	PROPN
american_scientific_journal-7485	21	1	[	[	X
american_scientific_journal-7485	21	2	3	3	NUM
american_scientific_journal-7485	21	3	]	]	PUNCT
american_scientific_journal-7485	21	4	,	,	PUNCT
american_scientific_journal-7485	21	5	a	a	DET
american_scientific_journal-7485	21	6	world	world	NOUN
american_scientific_journal-7485	21	7	famous	famous	ADJ
american_scientific_journal-7485	21	8	mathematician	mathematician	NOUN
american_scientific_journal-7485	21	9	interested	interested	ADJ
american_scientific_journal-7485	21	10	in	in	ADP
american_scientific_journal-7485	21	11	this	this	DET
american_scientific_journal-7485	21	12	unsolved	unsolved	ADJ
american_scientific_journal-7485	21	13	problem	problem	NOUN
american_scientific_journal-7485	21	14	.	.	PUNCT
american_scientific_journal-7485	22	1	for	for	ADP
american_scientific_journal-7485	22	2	more	more	ADJ
american_scientific_journal-7485	22	3	on	on	ADP
american_scientific_journal-7485	22	4	the	the	DET
american_scientific_journal-7485	22	5	collatz	collatz	NOUN
american_scientific_journal-7485	22	6	conjecture	conjecture	NOUN
american_scientific_journal-7485	22	7	see	see	VERB
american_scientific_journal-7485	22	8	[	[	X
american_scientific_journal-7485	22	9	4	4	NUM
american_scientific_journal-7485	22	10	,	,	PUNCT
american_scientific_journal-7485	22	11	5	5	NUM
american_scientific_journal-7485	22	12	,	,	PUNCT
american_scientific_journal-7485	22	13	6	6	NUM
american_scientific_journal-7485	22	14	]	]	PUNCT
american_scientific_journal-7485	22	15	.	.	PUNCT
american_scientific_journal-7485	23	1	this	this	DET
american_scientific_journal-7485	23	2	article	article	NOUN
american_scientific_journal-7485	23	3	is	be	AUX
american_scientific_journal-7485	23	4	specifically	specifically	ADV
american_scientific_journal-7485	23	5	based	base	VERB
american_scientific_journal-7485	23	6	on	on	ADP
american_scientific_journal-7485	23	7	a	a	DET
american_scientific_journal-7485	23	8	novel	novel	NOUN
american_scientific_journal-7485	23	9	theorem	theorem	VERB
american_scientific_journal-7485	23	10	.	.	PUNCT
american_scientific_journal-7485	24	1	so	so	ADV
american_scientific_journal-7485	24	2	by	by	ADP
american_scientific_journal-7485	24	3	adding	add	VERB
american_scientific_journal-7485	24	4	three	three	NUM
american_scientific_journal-7485	24	5	novel	novel	ADJ
american_scientific_journal-7485	24	6	theorems	theorem	NOUN
american_scientific_journal-7485	24	7	to	to	PART
american_scientific_journal-7485	24	8	analyze	analyze	VERB
american_scientific_journal-7485	24	9	the	the	DET
american_scientific_journal-7485	24	10	iterations	iteration	NOUN
american_scientific_journal-7485	24	11	of	of	ADP
american_scientific_journal-7485	24	12	numbers	number	NOUN
american_scientific_journal-7485	24	13	in	in	ADP
american_scientific_journal-7485	24	14	the	the	DET
american_scientific_journal-7485	24	15	collatz	collatz	NOUN
american_scientific_journal-7485	24	16	conjecture	conjecture	VERB
american_scientific_journal-7485	24	17	through	through	ADP
american_scientific_journal-7485	24	18	a	a	DET
american_scientific_journal-7485	24	19	3	3	NUM
american_scientific_journal-7485	24	20	column	column	NOUN
american_scientific_journal-7485	24	21	structure	structure	NOUN
american_scientific_journal-7485	24	22	[	[	AUX
american_scientific_journal-7485	24	23	see	see	VERB
american_scientific_journal-7485	24	24	figure	figure	NOUN
american_scientific_journal-7485	24	25	1	1	NUM
american_scientific_journal-7485	24	26	]	]	PUNCT
american_scientific_journal-7485	24	27	approach	approach	NOUN
american_scientific_journal-7485	24	28	which	which	PRON
american_scientific_journal-7485	24	29	explains	explain	VERB
american_scientific_journal-7485	24	30	the	the	DET
american_scientific_journal-7485	24	31	interactions	interaction	NOUN
american_scientific_journal-7485	24	32	between	between	ADP
american_scientific_journal-7485	24	33	3	3	NUM
american_scientific_journal-7485	24	34	columns	column	NOUN
american_scientific_journal-7485	24	35	.	.	PUNCT
american_scientific_journal-7485	25	1	an	an	DET
american_scientific_journal-7485	25	2	illustration	illustration	NOUN
american_scientific_journal-7485	25	3	[	[	X
american_scientific_journal-7485	25	4	see	see	INTJ
american_scientific_journal-7485	25	5	figure	figure	NOUN
american_scientific_journal-7485	25	6	2	2	NUM
american_scientific_journal-7485	25	7	]	]	PUNCT
american_scientific_journal-7485	25	8	also	also	ADV
american_scientific_journal-7485	25	9	shows	show	VERB
american_scientific_journal-7485	25	10	a	a	DET
american_scientific_journal-7485	25	11	pattern	pattern	NOUN
american_scientific_journal-7485	25	12	in	in	ADP
american_scientific_journal-7485	25	13	the	the	DET
american_scientific_journal-7485	25	14	projection	projection	NOUN
american_scientific_journal-7485	25	15	of	of	ADP
american_scientific_journal-7485	25	16	odd	odd	ADJ
american_scientific_journal-7485	25	17	and	and	CCONJ
american_scientific_journal-7485	25	18	even	even	ADV
american_scientific_journal-7485	25	19	numbers	number	NOUN
american_scientific_journal-7485	25	20	within	within	ADP
american_scientific_journal-7485	25	21	and	and	CCONJ
american_scientific_journal-7485	25	22	between	between	ADP
american_scientific_journal-7485	25	23	the	the	DET
american_scientific_journal-7485	25	24	3	3	NUM
american_scientific_journal-7485	25	25	columns	column	NOUN
american_scientific_journal-7485	25	26	’	'	PUNCT
american_scientific_journal-7485	25	27	properties	property	NOUN
american_scientific_journal-7485	25	28	.	.	PUNCT
american_scientific_journal-7485	26	1	in	in	ADP
american_scientific_journal-7485	26	2	this	this	DET
american_scientific_journal-7485	26	3	proof	proof	NOUN
american_scientific_journal-7485	26	4	,	,	PUNCT
american_scientific_journal-7485	26	5	the	the	DET
american_scientific_journal-7485	26	6	main	main	ADJ
american_scientific_journal-7485	26	7	notions	notion	NOUN
american_scientific_journal-7485	26	8	which	which	PRON
american_scientific_journal-7485	26	9	we	we	PRON
american_scientific_journal-7485	26	10	are	be	AUX
american_scientific_journal-7485	26	11	using	use	VERB
american_scientific_journal-7485	26	12	are	be	AUX
american_scientific_journal-7485	26	13	defined	define	VERB
american_scientific_journal-7485	26	14	as	as	SCONJ
american_scientific_journal-7485	26	15	follows	follow	VERB
american_scientific_journal-7485	26	16	:	:	PUNCT
american_scientific_journal-7485	26	17	to	to	PART
american_scientific_journal-7485	26	18	explain	explain	VERB
american_scientific_journal-7485	26	19	this	this	DET
american_scientific_journal-7485	26	20	conjecture	conjecture	NOUN
american_scientific_journal-7485	26	21	,	,	PUNCT
american_scientific_journal-7485	26	22	we	we	PRON
american_scientific_journal-7485	26	23	construct	construct	VERB
american_scientific_journal-7485	26	24	a	a	DET
american_scientific_journal-7485	26	25	three	three	NUM
american_scientific_journal-7485	26	26	column	column	NOUN
american_scientific_journal-7485	26	27	structure	structure	NOUN
american_scientific_journal-7485	26	28	of	of	ADP
american_scientific_journal-7485	26	29	numbers	number	NOUN
american_scientific_journal-7485	26	30	which	which	PRON
american_scientific_journal-7485	26	31	will	will	AUX
american_scientific_journal-7485	26	32	help	help	VERB
american_scientific_journal-7485	26	33	us	we	PRON
american_scientific_journal-7485	26	34	in	in	ADP
american_scientific_journal-7485	26	35	following	follow	VERB
american_scientific_journal-7485	26	36	the	the	DET
american_scientific_journal-7485	26	37	projections	projection	NOUN
american_scientific_journal-7485	26	38	.	.	PUNCT
american_scientific_journal-7485	27	1	the	the	DET
american_scientific_journal-7485	27	2	three	three	NUM
american_scientific_journal-7485	27	3	column	column	NOUN
american_scientific_journal-7485	27	4	structure	structure	NOUN
american_scientific_journal-7485	27	5	is	be	AUX
american_scientific_journal-7485	27	6	as	as	SCONJ
american_scientific_journal-7485	27	7	follows	follow	VERB
american_scientific_journal-7485	27	8	.	.	PUNCT
american_scientific_journal-7485	28	1	c1	c1	NOUN
american_scientific_journal-7485	28	2	:	:	PUNCT
american_scientific_journal-7485	29	1	[	[	X
american_scientific_journal-7485	29	2	1	1	NUM
american_scientific_journal-7485	29	3	4	4	NUM
american_scientific_journal-7485	29	4	7	7	NUM
american_scientific_journal-7485	29	5	10	10	NUM
american_scientific_journal-7485	29	6	13	13	NUM
american_scientific_journal-7485	29	7	16	16	NUM
american_scientific_journal-7485	29	8	19	19	NUM
american_scientific_journal-7485	29	9	22	22	NUM
american_scientific_journal-7485	29	10	25	25	NUM
american_scientific_journal-7485	29	11	·	·	PUNCT
american_scientific_journal-7485	29	12	·	·	PUNCT
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american_scientific_journal-7485	30	1	t	t	X
american_scientific_journal-7485	30	2	,	,	PUNCT
american_scientific_journal-7485	30	3	odd	odd	ADJ
american_scientific_journal-7485	30	4	and	and	CCONJ
american_scientific_journal-7485	30	5	even	even	ADV
american_scientific_journal-7485	30	6	c2	c2	PROPN
american_scientific_journal-7485	30	7	:	:	PUNCT
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american_scientific_journal-7485	31	2	2	2	NUM
american_scientific_journal-7485	31	3	5	5	NUM
american_scientific_journal-7485	31	4	8	8	NUM
american_scientific_journal-7485	31	5	11	11	NUM
american_scientific_journal-7485	31	6	14	14	NUM
american_scientific_journal-7485	31	7	17	17	NUM
american_scientific_journal-7485	31	8	20	20	NUM
american_scientific_journal-7485	31	9	23	23	NUM
american_scientific_journal-7485	31	10	26	26	NUM
american_scientific_journal-7485	31	11	·	·	PUNCT
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american_scientific_journal-7485	31	13	·	·	PUNCT
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american_scientific_journal-7485	32	1	t	t	X
american_scientific_journal-7485	32	2	,	,	PUNCT
american_scientific_journal-7485	32	3	odd	odd	ADJ
american_scientific_journal-7485	32	4	and	and	CCONJ
american_scientific_journal-7485	32	5	even	even	ADV
american_scientific_journal-7485	32	6	c3	c3	X
american_scientific_journal-7485	32	7	:	:	PUNCT
american_scientific_journal-7485	33	1	[	[	X
american_scientific_journal-7485	33	2	3	3	NUM
american_scientific_journal-7485	33	3	6	6	NUM
american_scientific_journal-7485	33	4	9	9	NUM
american_scientific_journal-7485	33	5	12	12	NUM
american_scientific_journal-7485	33	6	15	15	NUM
american_scientific_journal-7485	33	7	18	18	NUM
american_scientific_journal-7485	33	8	21	21	NUM
american_scientific_journal-7485	33	9	24	24	NUM
american_scientific_journal-7485	33	10	27	27	NUM
american_scientific_journal-7485	33	11	·	·	PUNCT
american_scientific_journal-7485	33	12	·	·	PUNCT
american_scientific_journal-7485	33	13	·	·	PUNCT
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american_scientific_journal-7485	34	1	t	t	X
american_scientific_journal-7485	34	2	,	,	PUNCT
american_scientific_journal-7485	34	3	odd	odd	ADJ
american_scientific_journal-7485	34	4	and	and	CCONJ
american_scientific_journal-7485	34	5	even	even	ADV
american_scientific_journal-7485	34	6	.	.	PUNCT
american_scientific_journal-7485	35	1	where	where	SCONJ
american_scientific_journal-7485	35	2	t	t	PROPN
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american_scientific_journal-7485	35	4	the	the	DET
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american_scientific_journal-7485	35	9	.	.	PUNCT
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american_scientific_journal-7485	36	3	and	and	CCONJ
american_scientific_journal-7485	36	4	odd	odd	ADJ
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american_scientific_journal-7485	36	6	in	in	ADP
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american_scientific_journal-7485	36	10	.	.	PUNCT
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american_scientific_journal-7485	37	3	an	an	DET
american_scientific_journal-7485	37	4	even	even	ADJ
american_scientific_journal-7485	37	5	number	number	NOUN
american_scientific_journal-7485	37	6	in	in	ADP
american_scientific_journal-7485	37	7	the	the	DET
american_scientific_journal-7485	37	8	specific	specific	ADJ
american_scientific_journal-7485	37	9	columns	column	NOUN
american_scientific_journal-7485	37	10	.	.	PUNCT
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american_scientific_journal-7485	38	5	journal	journal	NOUN
american_scientific_journal-7485	38	6	for	for	ADP
american_scientific_journal-7485	38	7	engineering	engineering	NOUN
american_scientific_journal-7485	38	8	,	,	PUNCT
american_scientific_journal-7485	38	9	technology	technology	NOUN
american_scientific_journal-7485	38	10	,	,	PUNCT
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american_scientific_journal-7485	38	12	sciences	science	NOUN
american_scientific_journal-7485	38	13	(	(	PUNCT
american_scientific_journal-7485	38	14	asrjets	asrjet	NOUN
american_scientific_journal-7485	38	15	)	)	PUNCT
american_scientific_journal-7485	38	16	(	(	PUNCT
american_scientific_journal-7485	38	17	2022	2022	NUM
american_scientific_journal-7485	38	18	)	)	PUNCT
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american_scientific_journal-7485	38	20	88	88	NUM
american_scientific_journal-7485	38	21	,	,	PUNCT
american_scientific_journal-7485	38	22	no	no	DET
american_scientific_journal-7485	38	23	1	1	NUM
american_scientific_journal-7485	38	24	,	,	PUNCT
american_scientific_journal-7485	38	25	pp	pp	ADV
american_scientific_journal-7485	38	26	91	91	NUM
american_scientific_journal-7485	38	27	-	-	SYM
american_scientific_journal-7485	38	28	98	98	NUM
american_scientific_journal-7485	38	29	93	93	NUM
american_scientific_journal-7485	38	30	figure	figure	NOUN
american_scientific_journal-7485	38	31	1	1	NUM
american_scientific_journal-7485	38	32	:	:	PUNCT
american_scientific_journal-7485	38	33	the	the	DET
american_scientific_journal-7485	38	34	3	3	NUM
american_scientific_journal-7485	38	35	column	column	NOUN
american_scientific_journal-7485	38	36	structure	structure	NOUN
american_scientific_journal-7485	38	37	explained	explain	VERB
american_scientific_journal-7485	38	38	.	.	PUNCT
american_scientific_journal-7485	39	1	*	*	PUNCT
american_scientific_journal-7485	39	2	note	note	VERB
american_scientific_journal-7485	39	3	that	that	SCONJ
american_scientific_journal-7485	39	4	the	the	DET
american_scientific_journal-7485	39	5	numbers	number	NOUN
american_scientific_journal-7485	39	6	highlighted	highlight	VERB
american_scientific_journal-7485	39	7	in	in	ADP
american_scientific_journal-7485	39	8	red	red	PROPN
american_scientific_journal-7485	39	9	represent	represent	VERB
american_scientific_journal-7485	39	10	prime	prime	ADJ
american_scientific_journal-7485	39	11	numbers	number	NOUN
american_scientific_journal-7485	39	12	,	,	PUNCT
american_scientific_journal-7485	39	13	present	present	ADJ
american_scientific_journal-7485	39	14	only	only	ADV
american_scientific_journal-7485	39	15	in	in	ADP
american_scientific_journal-7485	39	16	column	column	NOUN
american_scientific_journal-7485	39	17	c1	c1	PROPN
american_scientific_journal-7485	39	18	and	and	CCONJ
american_scientific_journal-7485	39	19	c2	c2	PROPN
american_scientific_journal-7485	39	20	.	.	PUNCT
american_scientific_journal-7485	40	1	where	where	SCONJ
american_scientific_journal-7485	40	2	t	t	PROPN
american_scientific_journal-7485	40	3	is	be	AUX
american_scientific_journal-7485	40	4	the	the	DET
american_scientific_journal-7485	40	5	transpose	transpose	NOUN
american_scientific_journal-7485	40	6	of	of	ADP
american_scientific_journal-7485	40	7	the	the	DET
american_scientific_journal-7485	40	8	array	array	NOUN
american_scientific_journal-7485	40	9	.	.	PUNCT
american_scientific_journal-7485	41	1	we	we	PRON
american_scientific_journal-7485	41	2	now	now	ADV
american_scientific_journal-7485	41	3	fix	fix	VERB
american_scientific_journal-7485	41	4	some	some	DET
american_scientific_journal-7485	41	5	notations	notation	NOUN
american_scientific_journal-7485	41	6	following	follow	VERB
american_scientific_journal-7485	41	7	figure	figure	NOUN
american_scientific_journal-7485	41	8	.	.	PUNCT
american_scientific_journal-7485	42	1	we	we	PRON
american_scientific_journal-7485	42	2	set	set	VERB
american_scientific_journal-7485	42	3	c1	c1	PROPN
american_scientific_journal-7485	42	4	to	to	PART
american_scientific_journal-7485	42	5	mean	mean	VERB
american_scientific_journal-7485	42	6	a	a	DET
american_scientific_journal-7485	42	7	number	number	NOUN
american_scientific_journal-7485	42	8	in	in	ADP
american_scientific_journal-7485	42	9	column	column	NOUN
american_scientific_journal-7485	42	10	1	1	NUM
american_scientific_journal-7485	42	11	,	,	PUNCT
american_scientific_journal-7485	42	12			DET
american_scientific_journal-7485	42	13	c1	c1	PROPN
american_scientific_journal-7485	42	14	-	-	PUNCT
american_scientific_journal-7485	42	15	0	0	NUM
american_scientific_journal-7485	42	16	mean	mean	VERB
american_scientific_journal-7485	42	17	an	an	DET
american_scientific_journal-7485	42	18	odd	odd	ADJ
american_scientific_journal-7485	42	19	number	number	NOUN
american_scientific_journal-7485	42	20	in	in	ADP
american_scientific_journal-7485	42	21	column	column	NOUN
american_scientific_journal-7485	42	22	1	1	NUM
american_scientific_journal-7485	42	23	,	,	PUNCT
american_scientific_journal-7485	42	24			PRON
american_scientific_journal-7485	42	25	c1	c1	PROPN
american_scientific_journal-7485	42	26	-	-	PUNCT
american_scientific_journal-7485	42	27	e	e	PROPN
american_scientific_journal-7485	42	28	mean	mean	VERB
american_scientific_journal-7485	42	29	an	an	DET
american_scientific_journal-7485	42	30	even	even	ADJ
american_scientific_journal-7485	42	31	number	number	NOUN
american_scientific_journal-7485	42	32	in	in	ADP
american_scientific_journal-7485	42	33	column	column	NOUN
american_scientific_journal-7485	42	34	1	1	NUM
american_scientific_journal-7485	42	35	.	.	PUNCT
american_scientific_journal-7485	43	1	let	let	VERB
american_scientific_journal-7485	43	2	c2	c2	PROPN
american_scientific_journal-7485	43	3	mean	mean	VERB
american_scientific_journal-7485	43	4	a	a	DET
american_scientific_journal-7485	43	5	number	number	NOUN
american_scientific_journal-7485	43	6	in	in	ADP
american_scientific_journal-7485	43	7	column	column	NOUN
american_scientific_journal-7485	43	8	2	2	NUM
american_scientific_journal-7485	43	9	,	,	PUNCT
american_scientific_journal-7485	43	10			PRON
american_scientific_journal-7485	43	11	c2	c2	PROPN
american_scientific_journal-7485	43	12	-	-	PUNCT
american_scientific_journal-7485	43	13	0	0	NUM
american_scientific_journal-7485	43	14	mean	mean	VERB
american_scientific_journal-7485	43	15	an	an	DET
american_scientific_journal-7485	43	16	odd	odd	ADJ
american_scientific_journal-7485	43	17	number	number	NOUN
american_scientific_journal-7485	43	18	in	in	ADP
american_scientific_journal-7485	43	19	column	column	NOUN
american_scientific_journal-7485	43	20	2	2	NUM
american_scientific_journal-7485	43	21	,	,	PUNCT
american_scientific_journal-7485	43	22			PRON
american_scientific_journal-7485	43	23	c2	c2	PROPN
american_scientific_journal-7485	43	24	-	-	PUNCT
american_scientific_journal-7485	43	25	e	e	PROPN
american_scientific_journal-7485	43	26	mean	mean	VERB
american_scientific_journal-7485	43	27	an	an	DET
american_scientific_journal-7485	43	28	even	even	ADJ
american_scientific_journal-7485	43	29	number	number	NOUN
american_scientific_journal-7485	43	30	in	in	ADP
american_scientific_journal-7485	43	31	column	column	NOUN
american_scientific_journal-7485	43	32	2	2	NUM
american_scientific_journal-7485	43	33	.	.	PUNCT
american_scientific_journal-7485	44	1	let	let	VERB
american_scientific_journal-7485	44	2	c3	c3	PROPN
american_scientific_journal-7485	44	3	mean	mean	VERB
american_scientific_journal-7485	44	4	a	a	DET
american_scientific_journal-7485	44	5	number	number	NOUN
american_scientific_journal-7485	44	6	in	in	ADP
american_scientific_journal-7485	44	7	column	column	NOUN
american_scientific_journal-7485	44	8	3	3	NUM
american_scientific_journal-7485	44	9	,	,	PUNCT
american_scientific_journal-7485	44	10			PRON
american_scientific_journal-7485	44	11	c3	c3	PROPN
american_scientific_journal-7485	44	12	-	-	PROPN
american_scientific_journal-7485	44	13	0	0	NUM
american_scientific_journal-7485	44	14	mean	mean	VERB
american_scientific_journal-7485	44	15	an	an	DET
american_scientific_journal-7485	44	16	odd	odd	ADJ
american_scientific_journal-7485	44	17	number	number	NOUN
american_scientific_journal-7485	44	18	in	in	ADP
american_scientific_journal-7485	44	19	column	column	NOUN
american_scientific_journal-7485	44	20	3	3	NUM
american_scientific_journal-7485	44	21	,	,	PUNCT
american_scientific_journal-7485	44	22			PRON
american_scientific_journal-7485	44	23	c3	c3	PROPN
american_scientific_journal-7485	44	24	-	-	PUNCT
american_scientific_journal-7485	44	25	e	e	NOUN
american_scientific_journal-7485	44	26	mean	mean	VERB
american_scientific_journal-7485	44	27	an	an	DET
american_scientific_journal-7485	44	28	even	even	ADJ
american_scientific_journal-7485	44	29	number	number	NOUN
american_scientific_journal-7485	44	30	in	in	ADP
american_scientific_journal-7485	44	31	column	column	NOUN
american_scientific_journal-7485	44	32	3	3	NUM
american_scientific_journal-7485	44	33	.	.	PUNCT
american_scientific_journal-7485	45	1	american	american	ADJ
american_scientific_journal-7485	45	2	academic	academic	ADJ
american_scientific_journal-7485	45	3	scientific	scientific	ADJ
american_scientific_journal-7485	45	4	research	research	NOUN
american_scientific_journal-7485	45	5	journal	journal	NOUN
american_scientific_journal-7485	45	6	for	for	ADP
american_scientific_journal-7485	45	7	engineering	engineering	NOUN
american_scientific_journal-7485	45	8	,	,	PUNCT
american_scientific_journal-7485	45	9	technology	technology	NOUN
american_scientific_journal-7485	45	10	,	,	PUNCT
american_scientific_journal-7485	45	11	and	and	CCONJ
american_scientific_journal-7485	45	12	sciences	science	NOUN
american_scientific_journal-7485	45	13	(	(	PUNCT
american_scientific_journal-7485	45	14	asrjets	asrjet	NOUN
american_scientific_journal-7485	45	15	)	)	PUNCT
american_scientific_journal-7485	45	16	(	(	PUNCT
american_scientific_journal-7485	45	17	2022	2022	NUM
american_scientific_journal-7485	45	18	)	)	PUNCT
american_scientific_journal-7485	45	19	volume	volume	NOUN
american_scientific_journal-7485	45	20	88	88	NUM
american_scientific_journal-7485	45	21	,	,	PUNCT
american_scientific_journal-7485	45	22	no	no	DET
american_scientific_journal-7485	45	23	1	1	NUM
american_scientific_journal-7485	45	24	,	,	PUNCT
american_scientific_journal-7485	45	25	pp	pp	ADV
american_scientific_journal-7485	45	26	91	91	NUM
american_scientific_journal-7485	45	27	-	-	SYM
american_scientific_journal-7485	45	28	98	98	NUM
american_scientific_journal-7485	45	29	94	94	NUM
american_scientific_journal-7485	45	30	2	2	NUM
american_scientific_journal-7485	45	31	.	.	PUNCT
american_scientific_journal-7485	45	32	main	main	ADJ
american_scientific_journal-7485	45	33	section	section	NOUN
american_scientific_journal-7485	45	34	let	let	VERB
american_scientific_journal-7485	45	35	us	we	PRON
american_scientific_journal-7485	45	36	start	start	VERB
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american_scientific_journal-7485	45	41	structure	structure	NOUN
american_scientific_journal-7485	45	42	of	of	ADP
american_scientific_journal-7485	45	43	numbers	number	NOUN
american_scientific_journal-7485	45	44	[	[	X
american_scientific_journal-7485	45	45	see	see	VERB
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american_scientific_journal-7485	45	47	1	1	NUM
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american_scientific_journal-7485	45	50	:	:	PUNCT
american_scientific_journal-7485	46	1	[	[	X
american_scientific_journal-7485	46	2	1	1	NUM
american_scientific_journal-7485	46	3	4	4	NUM
american_scientific_journal-7485	46	4	7	7	NUM
american_scientific_journal-7485	46	5	10	10	NUM
american_scientific_journal-7485	46	6	13	13	NUM
american_scientific_journal-7485	46	7	16	16	NUM
american_scientific_journal-7485	46	8	19	19	NUM
american_scientific_journal-7485	46	9	22	22	NUM
american_scientific_journal-7485	46	10	25	25	NUM
american_scientific_journal-7485	46	11	·	·	PUNCT
american_scientific_journal-7485	46	12	·	·	PUNCT
american_scientific_journal-7485	46	13	·	·	PUNCT
american_scientific_journal-7485	46	14	]	]	PUNCT
american_scientific_journal-7485	47	1	t	t	X
american_scientific_journal-7485	47	2	,	,	PUNCT
american_scientific_journal-7485	47	3	odd	odd	ADJ
american_scientific_journal-7485	47	4	and	and	CCONJ
american_scientific_journal-7485	47	5	even	even	ADV
american_scientific_journal-7485	47	6	c2	c2	PROPN
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american_scientific_journal-7485	48	2	2	2	NUM
american_scientific_journal-7485	48	3	5	5	NUM
american_scientific_journal-7485	48	4	8	8	NUM
american_scientific_journal-7485	48	5	11	11	NUM
american_scientific_journal-7485	48	6	14	14	NUM
american_scientific_journal-7485	48	7	17	17	NUM
american_scientific_journal-7485	48	8	20	20	NUM
american_scientific_journal-7485	48	9	23	23	NUM
american_scientific_journal-7485	48	10	26	26	NUM
american_scientific_journal-7485	48	11	·	·	PUNCT
american_scientific_journal-7485	48	12	·	·	PUNCT
american_scientific_journal-7485	48	13	·	·	PUNCT
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american_scientific_journal-7485	49	1	t	t	X
american_scientific_journal-7485	49	2	,	,	PUNCT
american_scientific_journal-7485	49	3	odd	odd	ADJ
american_scientific_journal-7485	49	4	and	and	CCONJ
american_scientific_journal-7485	49	5	even	even	ADV
american_scientific_journal-7485	49	6	c3	c3	PROPN
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american_scientific_journal-7485	50	2	3	3	NUM
american_scientific_journal-7485	50	3	6	6	NUM
american_scientific_journal-7485	50	4	9	9	NUM
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american_scientific_journal-7485	50	6	15	15	NUM
american_scientific_journal-7485	50	7	18	18	NUM
american_scientific_journal-7485	50	8	21	21	NUM
american_scientific_journal-7485	50	9	24	24	NUM
american_scientific_journal-7485	50	10	27	27	NUM
american_scientific_journal-7485	50	11	·	·	PUNCT
american_scientific_journal-7485	50	12	·	·	PUNCT
american_scientific_journal-7485	50	13	·	·	PUNCT
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american_scientific_journal-7485	50	15	t	t	PROPN
american_scientific_journal-7485	50	16	,	,	PUNCT
american_scientific_journal-7485	50	17	odd	odd	ADJ
american_scientific_journal-7485	50	18	and	and	CCONJ
american_scientific_journal-7485	50	19	even	even	ADV
american_scientific_journal-7485	50	20	.	.	PUNCT
american_scientific_journal-7485	51	1	we	we	PRON
american_scientific_journal-7485	51	2	know	know	VERB
american_scientific_journal-7485	51	3	that	that	SCONJ
american_scientific_journal-7485	51	4	in	in	ADP
american_scientific_journal-7485	51	5	the	the	DET
american_scientific_journal-7485	51	6	collatz	collatz	NOUN
american_scientific_journal-7485	51	7	conjecture	conjecture	NOUN
american_scientific_journal-7485	51	8	,	,	PUNCT
american_scientific_journal-7485	51	9	if	if	SCONJ
american_scientific_journal-7485	51	10	n	n	PRON
american_scientific_journal-7485	51	11	is	be	AUX
american_scientific_journal-7485	51	12	odd	odd	ADJ
american_scientific_journal-7485	51	13	,	,	PUNCT
american_scientific_journal-7485	51	14	then	then	ADV
american_scientific_journal-7485	51	15	we	we	PRON
american_scientific_journal-7485	51	16	have	have	VERB
american_scientific_journal-7485	51	17	two	two	NUM
american_scientific_journal-7485	51	18	operations	operation	NOUN
american_scientific_journal-7485	51	19	:	:	PUNCT
american_scientific_journal-7485	51	20	magnification	magnification	NOUN
american_scientific_journal-7485	51	21	by	by	ADP
american_scientific_journal-7485	51	22	3	3	NUM
american_scientific_journal-7485	51	23	and	and	CCONJ
american_scientific_journal-7485	51	24	then	then	ADV
american_scientific_journal-7485	51	25	translation	translation	NOUN
american_scientific_journal-7485	51	26	by	by	ADP
american_scientific_journal-7485	51	27	one	one	NUM
american_scientific_journal-7485	51	28	.	.	PUNCT
american_scientific_journal-7485	52	1	in	in	ADP
american_scientific_journal-7485	52	2	other	other	ADJ
american_scientific_journal-7485	52	3	words	word	NOUN
american_scientific_journal-7485	52	4	n	n	CCONJ
american_scientific_journal-7485	52	5	odd	odd	ADJ
american_scientific_journal-7485	52	6	is	be	AUX
american_scientific_journal-7485	52	7	projected	project	VERB
american_scientific_journal-7485	52	8	to	to	ADP
american_scientific_journal-7485	52	9	an	an	DET
american_scientific_journal-7485	52	10	even	even	ADJ
american_scientific_journal-7485	52	11	number	number	NOUN
american_scientific_journal-7485	52	12	.	.	PUNCT
american_scientific_journal-7485	53	1	we	we	PRON
american_scientific_journal-7485	53	2	also	also	ADV
american_scientific_journal-7485	53	3	know	know	VERB
american_scientific_journal-7485	53	4	if	if	SCONJ
american_scientific_journal-7485	53	5	n	n	PRON
american_scientific_journal-7485	53	6	is	be	AUX
american_scientific_journal-7485	53	7	even	even	ADV
american_scientific_journal-7485	53	8	,	,	PUNCT
american_scientific_journal-7485	53	9	then	then	ADV
american_scientific_journal-7485	53	10	we	we	PRON
american_scientific_journal-7485	53	11	divide	divide	VERB
american_scientific_journal-7485	53	12	it	it	PRON
american_scientific_journal-7485	53	13	by	by	ADP
american_scientific_journal-7485	53	14	two	two	NUM
american_scientific_journal-7485	53	15	until	until	SCONJ
american_scientific_journal-7485	53	16	it	it	PRON
american_scientific_journal-7485	53	17	projects	project	VERB
american_scientific_journal-7485	53	18	to	to	ADP
american_scientific_journal-7485	53	19	a	a	DET
american_scientific_journal-7485	53	20	column	column	NOUN
american_scientific_journal-7485	53	21	as	as	ADP
american_scientific_journal-7485	53	22	an	an	DET
american_scientific_journal-7485	53	23	odd	odd	ADJ
american_scientific_journal-7485	53	24	number	number	NOUN
american_scientific_journal-7485	53	25	.	.	PUNCT
american_scientific_journal-7485	54	1	figure	figure	NOUN
american_scientific_journal-7485	54	2	2	2	NUM
american_scientific_journal-7485	54	3	:	:	PUNCT
american_scientific_journal-7485	54	4	the	the	DET
american_scientific_journal-7485	54	5	rule	rule	NOUN
american_scientific_journal-7485	54	6	of	of	ADP
american_scientific_journal-7485	54	7	projection	projection	NOUN
american_scientific_journal-7485	54	8	of	of	ADP
american_scientific_journal-7485	54	9	numbers	number	NOUN
american_scientific_journal-7485	54	10	in	in	ADP
american_scientific_journal-7485	54	11	the	the	DET
american_scientific_journal-7485	54	12	collatz	collatz	NOUN
american_scientific_journal-7485	54	13	conjecture	conjecture	NOUN
american_scientific_journal-7485	54	14	.	.	PUNCT
american_scientific_journal-7485	55	1	from	from	ADP
american_scientific_journal-7485	55	2	figure	figure	NOUN
american_scientific_journal-7485	55	3	2	2	NUM
american_scientific_journal-7485	55	4	we	we	PRON
american_scientific_journal-7485	55	5	note	note	VERB
american_scientific_journal-7485	55	6			NOUN
american_scientific_journal-7485	55	7	red	red	ADJ
american_scientific_journal-7485	55	8	arrows	arrow	NOUN
american_scientific_journal-7485	55	9	represent	represent	VERB
american_scientific_journal-7485	55	10	the	the	DET
american_scientific_journal-7485	55	11	3n	3n	NUM
american_scientific_journal-7485	55	12	+	+	SYM
american_scientific_journal-7485	55	13	1	1	NUM
american_scientific_journal-7485	55	14	operations	operation	NOUN
american_scientific_journal-7485	55	15	between	between	ADP
american_scientific_journal-7485	55	16	numbers	number	NOUN
american_scientific_journal-7485	55	17	until	until	SCONJ
american_scientific_journal-7485	55	18	it	it	PRON
american_scientific_journal-7485	55	19	turns	turn	VERB
american_scientific_journal-7485	55	20	to	to	ADP
american_scientific_journal-7485	55	21	a	a	DET
american_scientific_journal-7485	55	22	green	green	ADJ
american_scientific_journal-7485	55	23	even	even	ADJ
american_scientific_journal-7485	55	24	value	value	NOUN
american_scientific_journal-7485	55	25	before	before	ADP
american_scientific_journal-7485	55	26	reaching	reach	VERB
american_scientific_journal-7485	55	27	1	1	NUM
american_scientific_journal-7485	55	28	in	in	ADP
american_scientific_journal-7485	55	29	c1	c1	PROPN
american_scientific_journal-7485	55	30	-	-	PUNCT
american_scientific_journal-7485	56	1	o.	o.	PROPN
american_scientific_journal-7485	56	2			NOUN
american_scientific_journal-7485	56	3	green	green	ADJ
american_scientific_journal-7485	56	4	arrows	arrow	NOUN
american_scientific_journal-7485	56	5	represent	represent	VERB
american_scientific_journal-7485	56	6	the	the	DET
american_scientific_journal-7485	56	7	n	n	PROPN
american_scientific_journal-7485	56	8	/	/	SYM
american_scientific_journal-7485	56	9	2	2	NUM
american_scientific_journal-7485	56	10	which	which	PRON
american_scientific_journal-7485	56	11	is	be	AUX
american_scientific_journal-7485	56	12	the	the	DET
american_scientific_journal-7485	56	13	positive	positive	ADJ
american_scientific_journal-7485	56	14	projections	projection	NOUN
american_scientific_journal-7485	56	15	towards	towards	ADP
american_scientific_journal-7485	56	16	lowering	lower	VERB
american_scientific_journal-7485	56	17	the	the	DET
american_scientific_journal-7485	56	18	value	value	NOUN
american_scientific_journal-7485	56	19	of	of	ADP
american_scientific_journal-7485	56	20	the	the	DET
american_scientific_journal-7485	56	21	upper	upper	ADJ
american_scientific_journal-7485	56	22	numbers	number	NOUN
american_scientific_journal-7485	56	23	to	to	PART
american_scientific_journal-7485	56	24	finally	finally	ADV
american_scientific_journal-7485	56	25	attain	attain	VERB
american_scientific_journal-7485	56	26	a	a	DET
american_scientific_journal-7485	56	27	value	value	NOUN
american_scientific_journal-7485	56	28	of	of	ADP
american_scientific_journal-7485	56	29	1	1	NUM
american_scientific_journal-7485	56	30	.	.	PUNCT
american_scientific_journal-7485	56	31			PROPN
american_scientific_journal-7485	57	1	c3	c3	PROPN
american_scientific_journal-7485	57	2	numbers	number	NOUN
american_scientific_journal-7485	57	3	,	,	PUNCT
american_scientific_journal-7485	57	4	projects	project	NOUN
american_scientific_journal-7485	57	5	to	to	ADP
american_scientific_journal-7485	57	6	themselves	themselves	PRON
american_scientific_journal-7485	57	7	as	as	ADP
american_scientific_journal-7485	57	8	even	even	ADV
american_scientific_journal-7485	57	9	numbers	number	NOUN
american_scientific_journal-7485	57	10	and	and	CCONJ
american_scientific_journal-7485	57	11	then	then	ADV
american_scientific_journal-7485	57	12	to	to	ADP
american_scientific_journal-7485	57	13	an	an	DET
american_scientific_journal-7485	57	14	odd	odd	ADJ
american_scientific_journal-7485	57	15	number	number	NOUN
american_scientific_journal-7485	57	16	which	which	PRON
american_scientific_journal-7485	57	17	finally	finally	ADV
american_scientific_journal-7485	57	18	projects	project	VERB
american_scientific_journal-7485	57	19	to	to	PART
american_scientific_journal-7485	57	20	c1american	c1american	VERB
american_scientific_journal-7485	57	21	academic	academic	ADJ
american_scientific_journal-7485	57	22	scientific	scientific	ADJ
american_scientific_journal-7485	57	23	research	research	NOUN
american_scientific_journal-7485	57	24	journal	journal	NOUN
american_scientific_journal-7485	57	25	for	for	ADP
american_scientific_journal-7485	57	26	engineering	engineering	NOUN
american_scientific_journal-7485	57	27	,	,	PUNCT
american_scientific_journal-7485	57	28	technology	technology	NOUN
american_scientific_journal-7485	57	29	,	,	PUNCT
american_scientific_journal-7485	57	30	and	and	CCONJ
american_scientific_journal-7485	57	31	sciences	science	NOUN
american_scientific_journal-7485	57	32	(	(	PUNCT
american_scientific_journal-7485	57	33	asrjets	asrjet	NOUN
american_scientific_journal-7485	57	34	)	)	PUNCT
american_scientific_journal-7485	57	35	(	(	PUNCT
american_scientific_journal-7485	57	36	2022	2022	NUM
american_scientific_journal-7485	57	37	)	)	PUNCT
american_scientific_journal-7485	57	38	volume	volume	NOUN
american_scientific_journal-7485	57	39	88	88	NUM
american_scientific_journal-7485	57	40	,	,	PUNCT
american_scientific_journal-7485	57	41	no	no	DET
american_scientific_journal-7485	57	42	1	1	NUM
american_scientific_journal-7485	57	43	,	,	PUNCT
american_scientific_journal-7485	57	44	pp	pp	ADV
american_scientific_journal-7485	57	45	91	91	NUM
american_scientific_journal-7485	57	46	-	-	SYM
american_scientific_journal-7485	57	47	98	98	NUM
american_scientific_journal-7485	57	48	95	95	NUM
american_scientific_journal-7485	57	49	e.	e.	NOUN
american_scientific_journal-7485	58	1	it	it	PRON
american_scientific_journal-7485	58	2	also	also	ADV
american_scientific_journal-7485	58	3	shows	show	VERB
american_scientific_journal-7485	58	4	c	c	PROPN
american_scientific_journal-7485	58	5	3	3	NUM
american_scientific_journal-7485	58	6	is	be	AUX
american_scientific_journal-7485	58	7	now	now	ADV
american_scientific_journal-7485	58	8	immune	immune	ADJ
american_scientific_journal-7485	58	9	against	against	ADP
american_scientific_journal-7485	58	10	receiving	receive	VERB
american_scientific_journal-7485	58	11	any	any	DET
american_scientific_journal-7485	58	12	projected	project	VERB
american_scientific_journal-7485	58	13	numbers	number	NOUN
american_scientific_journal-7485	58	14	.	.	PUNCT
american_scientific_journal-7485	59	1			PRON
american_scientific_journal-7485	59	2	projections	projection	NOUN
american_scientific_journal-7485	59	3	between	between	ADP
american_scientific_journal-7485	59	4	c2	c2	PROPN
american_scientific_journal-7485	59	5	-	-	PUNCT
american_scientific_journal-7485	59	6	o	o	PROPN
american_scientific_journal-7485	59	7	and	and	CCONJ
american_scientific_journal-7485	59	8	c1	c1	PROPN
american_scientific_journal-7485	59	9	-	-	PUNCT
american_scientific_journal-7485	59	10	e	e	PROPN
american_scientific_journal-7485	59	11	finally	finally	ADV
american_scientific_journal-7485	59	12	reach	reach	VERB
american_scientific_journal-7485	59	13	c2	c2	PROPN
american_scientific_journal-7485	59	14	-	-	PUNCT
american_scientific_journal-7485	59	15	e.	e.	PROPN
american_scientific_journal-7485	59	16			NOUN
american_scientific_journal-7485	59	17	projections	projection	NOUN
american_scientific_journal-7485	59	18	between	between	ADP
american_scientific_journal-7485	59	19	c2	c2	PROPN
american_scientific_journal-7485	59	20	-	-	PUNCT
american_scientific_journal-7485	59	21	e	e	PROPN
american_scientific_journal-7485	59	22	and	and	CCONJ
american_scientific_journal-7485	59	23	c1	c1	PROPN
american_scientific_journal-7485	59	24	-	-	PUNCT
american_scientific_journal-7485	59	25	e	e	PROPN
american_scientific_journal-7485	59	26	back	back	ADV
american_scientific_journal-7485	59	27	to	to	AUX
american_scientific_journal-7485	59	28	finally	finally	ADV
american_scientific_journal-7485	59	29	project	project	VERB
american_scientific_journal-7485	59	30	to	to	ADP
american_scientific_journal-7485	59	31	a	a	DET
american_scientific_journal-7485	59	32	c2e	c2e	NOUN
american_scientific_journal-7485	59	33	to	to	ADP
american_scientific_journal-7485	59	34	c1	c1	PROPN
american_scientific_journal-7485	59	35	-	-	PUNCT
american_scientific_journal-7485	59	36	o	o	PROPN
american_scientific_journal-7485	59	37	which	which	PRON
american_scientific_journal-7485	59	38	could	could	AUX
american_scientific_journal-7485	59	39	finally	finally	ADV
american_scientific_journal-7485	59	40	attain	attain	VERB
american_scientific_journal-7485	59	41	the	the	DET
american_scientific_journal-7485	59	42	value	value	NOUN
american_scientific_journal-7485	59	43	of	of	ADP
american_scientific_journal-7485	59	44	1	1	NUM
american_scientific_journal-7485	59	45	,	,	PUNCT
american_scientific_journal-7485	59	46	or	or	CCONJ
american_scientific_journal-7485	59	47	projecting	project	VERB
american_scientific_journal-7485	59	48	it	it	PRON
american_scientific_journal-7485	59	49	back	back	ADV
american_scientific_journal-7485	59	50	to	to	ADP
american_scientific_journal-7485	59	51	c1	c1	NOUN
american_scientific_journal-7485	59	52	-	-	PUNCT
american_scientific_journal-7485	59	53	e	e	PROPN
american_scientific_journal-7485	59	54	for	for	ADP
american_scientific_journal-7485	59	55	another	another	DET
american_scientific_journal-7485	59	56	operation	operation	NOUN
american_scientific_journal-7485	59	57	between	between	ADP
american_scientific_journal-7485	59	58	the	the	DET
american_scientific_journal-7485	59	59	sub	sub	NOUN
american_scientific_journal-7485	59	60	-	-	NOUN
american_scientific_journal-7485	59	61	columns	column	NOUN
american_scientific_journal-7485	59	62	.	.	PUNCT
american_scientific_journal-7485	60	1	we	we	PRON
american_scientific_journal-7485	60	2	now	now	ADV
american_scientific_journal-7485	60	3	discuss	discuss	VERB
american_scientific_journal-7485	60	4	the	the	DET
american_scientific_journal-7485	60	5	following	follow	VERB
american_scientific_journal-7485	60	6	six	six	NUM
american_scientific_journal-7485	60	7	projections	projection	NOUN
american_scientific_journal-7485	60	8	:	:	PUNCT
american_scientific_journal-7485	60	9	case	case	NOUN
american_scientific_journal-7485	60	10	1	1	NUM
american_scientific_journal-7485	60	11	:	:	PUNCT
american_scientific_journal-7485	60	12	the	the	DET
american_scientific_journal-7485	60	13	collatz	collatz	NOUN
american_scientific_journal-7485	60	14	number	number	NOUN
american_scientific_journal-7485	60	15	of	of	ADP
american_scientific_journal-7485	60	16	c3	c3	PROPN
american_scientific_journal-7485	60	17	-	-	PUNCT
american_scientific_journal-7485	60	18	e	e	PROPN
american_scientific_journal-7485	60	19	subclass	subclass	NOUN
american_scientific_journal-7485	60	20	is	be	AUX
american_scientific_journal-7485	60	21	always	always	ADV
american_scientific_journal-7485	60	22	projected	project	VERB
american_scientific_journal-7485	60	23	to	to	PART
american_scientific_journal-7485	60	24	become	become	VERB
american_scientific_journal-7485	60	25	a	a	DET
american_scientific_journal-7485	60	26	c3	c3	PROPN
american_scientific_journal-7485	60	27	-	-	NOUN
american_scientific_journal-7485	60	28	o	o	NOUN
american_scientific_journal-7485	60	29	subclass	subclass	NOUN
american_scientific_journal-7485	60	30	number	number	NOUN
american_scientific_journal-7485	60	31	with	with	ADP
american_scientific_journal-7485	60	32	no	no	DET
american_scientific_journal-7485	60	33	return	return	NOUN
american_scientific_journal-7485	60	34	path	path	NOUN
american_scientific_journal-7485	60	35	to	to	ADP
american_scientific_journal-7485	60	36	c3	c3	PROPN
american_scientific_journal-7485	60	37	-	-	PROPN
american_scientific_journal-7485	60	38	e.	e.	PROPN
american_scientific_journal-7485	60	39	the	the	DET
american_scientific_journal-7485	60	40	process	process	NOUN
american_scientific_journal-7485	60	41	may	may	AUX
american_scientific_journal-7485	60	42	end	end	VERB
american_scientific_journal-7485	60	43	with	with	ADP
american_scientific_journal-7485	60	44	one	one	NUM
american_scientific_journal-7485	60	45	iteration	iteration	NOUN
american_scientific_journal-7485	60	46	or	or	CCONJ
american_scientific_journal-7485	60	47	multiple	multiple	ADJ
american_scientific_journal-7485	60	48	iterations	iteration	NOUN
american_scientific_journal-7485	60	49	.	.	PUNCT
american_scientific_journal-7485	61	1	for	for	ADP
american_scientific_journal-7485	61	2	example	example	NOUN
american_scientific_journal-7485	61	3	:	:	PUNCT
american_scientific_journal-7485	61	4			NOUN
american_scientific_journal-7485	61	5	186	186	NUM
american_scientific_journal-7485	61	6	∈	∈	PROPN
american_scientific_journal-7485	61	7	c3	c3	PROPN
american_scientific_journal-7485	61	8	-	-	PUNCT
american_scientific_journal-7485	61	9	e	e	PROPN
american_scientific_journal-7485	61	10	reaches	reach	VERB
american_scientific_journal-7485	61	11	to	to	ADP
american_scientific_journal-7485	61	12	93	93	NUM
american_scientific_journal-7485	61	13	∈	∈	PROPN
american_scientific_journal-7485	61	14	c3	c3	PROPN
american_scientific_journal-7485	61	15	-	-	PROPN
american_scientific_journal-7485	61	16	o	o	PROPN
american_scientific_journal-7485	61	17	in	in	ADP
american_scientific_journal-7485	61	18	only	only	ADJ
american_scientific_journal-7485	61	19	iteration	iteration	NOUN
american_scientific_journal-7485	61	20	.	.	PUNCT
american_scientific_journal-7485	62	1			PRON
american_scientific_journal-7485	63	1	but	but	CCONJ
american_scientific_journal-7485	63	2	24	24	NUM
american_scientific_journal-7485	63	3	∈	∈	PROPN
american_scientific_journal-7485	63	4	c3	c3	PROPN
american_scientific_journal-7485	63	5	-	-	PUNCT
american_scientific_journal-7485	63	6	e	e	PROPN
american_scientific_journal-7485	63	7	in	in	ADP
american_scientific_journal-7485	63	8	the	the	DET
american_scientific_journal-7485	63	9	first	first	ADJ
american_scientific_journal-7485	63	10	iteration	iteration	NOUN
american_scientific_journal-7485	63	11	reaches	reach	VERB
american_scientific_journal-7485	63	12	12	12	NUM
american_scientific_journal-7485	63	13	∈	∈	PROPN
american_scientific_journal-7485	63	14	c3	c3	PROPN
american_scientific_journal-7485	63	15	-	-	PUNCT
american_scientific_journal-7485	63	16	e	e	PROPN
american_scientific_journal-7485	63	17	,	,	PUNCT
american_scientific_journal-7485	63	18	12	12	NUM
american_scientific_journal-7485	63	19	to	to	PART
american_scientific_journal-7485	63	20	6	6	NUM
american_scientific_journal-7485	63	21	∈	∈	PROPN
american_scientific_journal-7485	63	22	c3	c3	PROPN
american_scientific_journal-7485	63	23	-	-	PUNCT
american_scientific_journal-7485	63	24	e	e	PROPN
american_scientific_journal-7485	63	25	,	,	PUNCT
american_scientific_journal-7485	63	26			PRON
american_scientific_journal-7485	63	27	and	and	CCONJ
american_scientific_journal-7485	63	28	finally	finally	ADV
american_scientific_journal-7485	63	29	6	6	NUM
american_scientific_journal-7485	63	30	to	to	PART
american_scientific_journal-7485	63	31	3	3	NUM
american_scientific_journal-7485	63	32	∈	∈	PROPN
american_scientific_journal-7485	63	33	c3	c3	PROPN
american_scientific_journal-7485	63	34	-	-	PROPN
american_scientific_journal-7485	63	35	o.	o.	PROPN
american_scientific_journal-7485	63	36	case	case	NOUN
american_scientific_journal-7485	63	37	2	2	NUM
american_scientific_journal-7485	63	38	:	:	PUNCT
american_scientific_journal-7485	63	39	the	the	DET
american_scientific_journal-7485	63	40	collatz	collatz	NOUN
american_scientific_journal-7485	63	41	number	number	NOUN
american_scientific_journal-7485	63	42	of	of	ADP
american_scientific_journal-7485	63	43	c3	c3	PROPN
american_scientific_journal-7485	63	44	-	-	PROPN
american_scientific_journal-7485	63	45	o	o	PROPN
american_scientific_journal-7485	63	46	subclass	subclass	NOUN
american_scientific_journal-7485	63	47	operates	operate	VERB
american_scientific_journal-7485	63	48	with	with	ADP
american_scientific_journal-7485	63	49	magnification	magnification	NOUN
american_scientific_journal-7485	63	50	by	by	ADP
american_scientific_journal-7485	63	51	3	3	NUM
american_scientific_journal-7485	63	52	followed	follow	VERB
american_scientific_journal-7485	63	53	by	by	ADP
american_scientific_journal-7485	63	54	translation	translation	NOUN
american_scientific_journal-7485	63	55	of	of	ADP
american_scientific_journal-7485	63	56	one	one	NUM
american_scientific_journal-7485	63	57	and	and	CCONJ
american_scientific_journal-7485	63	58	are	be	AUX
american_scientific_journal-7485	63	59	always	always	ADV
american_scientific_journal-7485	63	60	projected	project	VERB
american_scientific_journal-7485	63	61	after	after	ADP
american_scientific_journal-7485	63	62	only	only	ADV
american_scientific_journal-7485	63	63	one	one	NUM
american_scientific_journal-7485	63	64	iteration	iteration	NOUN
american_scientific_journal-7485	63	65	to	to	PART
american_scientific_journal-7485	63	66	become	become	VERB
american_scientific_journal-7485	63	67	a	a	DET
american_scientific_journal-7485	63	68	c1	c1	NOUN
american_scientific_journal-7485	63	69	-	-	PUNCT
american_scientific_journal-7485	63	70	e	e	NOUN
american_scientific_journal-7485	63	71	number	number	NOUN
american_scientific_journal-7485	63	72	with	with	ADP
american_scientific_journal-7485	63	73	no	no	DET
american_scientific_journal-7485	63	74	return	return	NOUN
american_scientific_journal-7485	63	75	to	to	ADP
american_scientific_journal-7485	63	76	c3	c3	PROPN
american_scientific_journal-7485	63	77	.	.	PUNCT
american_scientific_journal-7485	64	1	for	for	ADP
american_scientific_journal-7485	64	2	example	example	NOUN
american_scientific_journal-7485	64	3	,	,	PUNCT
american_scientific_journal-7485	64	4	following	follow	VERB
american_scientific_journal-7485	64	5	the	the	DET
american_scientific_journal-7485	64	6	example	example	NOUN
american_scientific_journal-7485	64	7	in	in	ADP
american_scientific_journal-7485	64	8	case	case	NOUN
american_scientific_journal-7485	64	9	1	1	NUM
american_scientific_journal-7485	64	10	:	:	PUNCT
american_scientific_journal-7485	64	11			NOUN
american_scientific_journal-7485	64	12	3	3	NUM
american_scientific_journal-7485	64	13	∈	∈	PROPN
american_scientific_journal-7485	64	14	c3	c3	PROPN
american_scientific_journal-7485	64	15	-	-	PROPN
american_scientific_journal-7485	64	16	o	o	PROPN
american_scientific_journal-7485	64	17	is	be	AUX
american_scientific_journal-7485	64	18	projected	project	VERB
american_scientific_journal-7485	64	19	to	to	ADP
american_scientific_journal-7485	64	20	10	10	NUM
american_scientific_journal-7485	64	21	∈	∈	PROPN
american_scientific_journal-7485	64	22	c1	c1	PROPN
american_scientific_journal-7485	64	23	-	-	PUNCT
american_scientific_journal-7485	64	24	e.	e.	PROPN
american_scientific_journal-7485	64	25			PROPN
american_scientific_journal-7485	64	26	also	also	ADV
american_scientific_journal-7485	64	27	,	,	PUNCT
american_scientific_journal-7485	64	28	one	one	PRON
american_scientific_journal-7485	64	29	can	can	AUX
american_scientific_journal-7485	64	30	easily	easily	ADV
american_scientific_journal-7485	64	31	see	see	VERB
american_scientific_journal-7485	64	32	the	the	DET
american_scientific_journal-7485	64	33	following	follow	VERB
american_scientific_journal-7485	64	34	one	one	NUM
american_scientific_journal-7485	64	35	iteration	iteration	NOUN
american_scientific_journal-7485	64	36	projections	projection	NOUN
american_scientific_journal-7485	64	37	129	129	NUM
american_scientific_journal-7485	64	38	∈	∈	PROPN
american_scientific_journal-7485	64	39	c3	c3	PROPN
american_scientific_journal-7485	64	40	-	-	PROPN
american_scientific_journal-7485	64	41	o	o	PROPN
american_scientific_journal-7485	64	42	projected	project	VERB
american_scientific_journal-7485	64	43	to	to	ADP
american_scientific_journal-7485	64	44	388	388	NUM
american_scientific_journal-7485	64	45	∈	∈	PROPN
american_scientific_journal-7485	64	46	c1	c1	NOUN
american_scientific_journal-7485	64	47	-	-	PUNCT
american_scientific_journal-7485	64	48	e	e	PROPN
american_scientific_journal-7485	64	49	219	219	NUM
american_scientific_journal-7485	64	50	∈	∈	PROPN
american_scientific_journal-7485	64	51	c3	c3	PROPN
american_scientific_journal-7485	64	52	-	-	PROPN
american_scientific_journal-7485	64	53	o	o	PROPN
american_scientific_journal-7485	64	54	projected	project	VERB
american_scientific_journal-7485	64	55	to	to	ADP
american_scientific_journal-7485	64	56	658	658	NUM
american_scientific_journal-7485	64	57	∈	∈	PROPN
american_scientific_journal-7485	64	58	c1	c1	NOUN
american_scientific_journal-7485	64	59	-	-	PUNCT
american_scientific_journal-7485	64	60	e	e	PROPN
american_scientific_journal-7485	64	61	2373	2373	NUM
american_scientific_journal-7485	64	62	∈	∈	PROPN
american_scientific_journal-7485	64	63	c3	c3	PROPN
american_scientific_journal-7485	64	64	-	-	PROPN
american_scientific_journal-7485	64	65	o	o	PROPN
american_scientific_journal-7485	64	66	projected	project	VERB
american_scientific_journal-7485	64	67	to	to	ADP
american_scientific_journal-7485	64	68	7120	7120	NUM
american_scientific_journal-7485	64	69	∈	∈	PROPN
american_scientific_journal-7485	64	70	c1	c1	NOUN
american_scientific_journal-7485	64	71	-	-	PUNCT
american_scientific_journal-7485	64	72	e	e	PROPN
american_scientific_journal-7485	64	73			PRON
american_scientific_journal-7485	64	74	we	we	PRON
american_scientific_journal-7485	64	75	also	also	ADV
american_scientific_journal-7485	64	76	observe	observe	VERB
american_scientific_journal-7485	64	77	that	that	SCONJ
american_scientific_journal-7485	64	78	a	a	DET
american_scientific_journal-7485	64	79	number	number	NOUN
american_scientific_journal-7485	64	80	of	of	ADP
american_scientific_journal-7485	64	81	c3	c3	PROPN
american_scientific_journal-7485	64	82	class	class	NOUN
american_scientific_journal-7485	64	83	can	can	AUX
american_scientific_journal-7485	64	84	not	not	PART
american_scientific_journal-7485	64	85	ever	ever	ADV
american_scientific_journal-7485	64	86	be	be	AUX
american_scientific_journal-7485	64	87	a	a	DET
american_scientific_journal-7485	64	88	projection	projection	NOUN
american_scientific_journal-7485	64	89	of	of	ADP
american_scientific_journal-7485	64	90	a	a	DET
american_scientific_journal-7485	64	91	number	number	NOUN
american_scientific_journal-7485	64	92	of	of	ADP
american_scientific_journal-7485	64	93	c1	c1	PROPN
american_scientific_journal-7485	64	94	class	class	PROPN
american_scientific_journal-7485	64	95	or	or	CCONJ
american_scientific_journal-7485	64	96	c2	c2	PROPN
american_scientific_journal-7485	64	97	class	class	NOUN
american_scientific_journal-7485	64	98	.	.	PUNCT
american_scientific_journal-7485	65	1	moreover	moreover	ADV
american_scientific_journal-7485	65	2	,	,	PUNCT
american_scientific_journal-7485	65	3	c3	c3	PROPN
american_scientific_journal-7485	65	4	numbers	number	NOUN
american_scientific_journal-7485	65	5	are	be	AUX
american_scientific_journal-7485	65	6	thus	thus	ADV
american_scientific_journal-7485	65	7	now	now	ADV
american_scientific_journal-7485	65	8	isolated	isolate	VERB
american_scientific_journal-7485	65	9	outside	outside	ADV
american_scientific_journal-7485	65	10	of	of	ADP
american_scientific_journal-7485	65	11	c3	c3	PROPN
american_scientific_journal-7485	65	12	after	after	ADP
american_scientific_journal-7485	65	13	the	the	DET
american_scientific_journal-7485	65	14	above	above	ADJ
american_scientific_journal-7485	65	15	iterations	iteration	NOUN
american_scientific_journal-7485	65	16	to	to	PART
american_scientific_journal-7485	65	17	receive	receive	VERB
american_scientific_journal-7485	65	18	any	any	DET
american_scientific_journal-7485	65	19	projections	projection	NOUN
american_scientific_journal-7485	65	20	back	back	ADV
american_scientific_journal-7485	65	21	from	from	ADP
american_scientific_journal-7485	65	22	c1	c1	PROPN
american_scientific_journal-7485	65	23	and	and	CCONJ
american_scientific_journal-7485	65	24	c2	c2	PROPN
american_scientific_journal-7485	65	25	.	.	PUNCT
american_scientific_journal-7485	66	1	case	case	NOUN
american_scientific_journal-7485	66	2	3	3	NUM
american_scientific_journal-7485	66	3	:	:	PUNCT
american_scientific_journal-7485	66	4	the	the	DET
american_scientific_journal-7485	66	5	collatz	collatz	PROPN
american_scientific_journal-7485	66	6	projection	projection	NOUN
american_scientific_journal-7485	66	7	of	of	ADP
american_scientific_journal-7485	66	8	c1	c1	PROPN
american_scientific_journal-7485	66	9	-	-	PUNCT
american_scientific_journal-7485	66	10	e	e	NOUN
american_scientific_journal-7485	66	11	subclass	subclass	NOUN
american_scientific_journal-7485	66	12	numbers	number	NOUN
american_scientific_journal-7485	66	13	are	be	AUX
american_scientific_journal-7485	66	14	the	the	DET
american_scientific_journal-7485	66	15	numbers	number	NOUN
american_scientific_journal-7485	66	16	from	from	ADP
american_scientific_journal-7485	66	17	c2e	c2e	ADJ
american_scientific_journal-7485	66	18	subclass	subclass	NOUN
american_scientific_journal-7485	66	19	or	or	CCONJ
american_scientific_journal-7485	66	20	c2	c2	PROPN
american_scientific_journal-7485	66	21	-	-	PUNCT
american_scientific_journal-7485	66	22	o	o	NOUN
american_scientific_journal-7485	66	23	subclass	subclass	NOUN
american_scientific_journal-7485	66	24	,	,	PUNCT
american_scientific_journal-7485	66	25	and	and	CCONJ
american_scientific_journal-7485	66	26	requires	require	VERB
american_scientific_journal-7485	66	27	only	only	ADV
american_scientific_journal-7485	66	28	one	one	NUM
american_scientific_journal-7485	66	29	iteration	iteration	NOUN
american_scientific_journal-7485	66	30	.	.	PUNCT
american_scientific_journal-7485	67	1	for	for	ADP
american_scientific_journal-7485	67	2	example	example	NOUN
american_scientific_journal-7485	67	3	:	:	PUNCT
american_scientific_journal-7485	67	4			NOUN
american_scientific_journal-7485	67	5	(	(	PUNCT
american_scientific_journal-7485	67	6	i	i	NOUN
american_scientific_journal-7485	67	7	)	)	PUNCT
american_scientific_journal-7485	67	8	:	:	PUNCT
american_scientific_journal-7485	67	9	76	76	NUM
american_scientific_journal-7485	67	10	∈	∈	PROPN
american_scientific_journal-7485	67	11	c1	c1	NOUN
american_scientific_journal-7485	67	12	-	-	PUNCT
american_scientific_journal-7485	67	13	e	e	PROPN
american_scientific_journal-7485	67	14	is	be	AUX
american_scientific_journal-7485	67	15	projected	project	VERB
american_scientific_journal-7485	67	16	to	to	ADP
american_scientific_journal-7485	67	17	38	38	NUM
american_scientific_journal-7485	67	18	∈	∈	PROPN
american_scientific_journal-7485	67	19	c2	c2	PROPN
american_scientific_journal-7485	67	20	-	-	PUNCT
american_scientific_journal-7485	67	21	e	e	PROPN
american_scientific_journal-7485	67	22	,	,	PUNCT
american_scientific_journal-7485	67	23			PRON
american_scientific_journal-7485	67	24	(	(	PUNCT
american_scientific_journal-7485	67	25	ii	ii	NOUN
american_scientific_journal-7485	67	26	)	)	PUNCT
american_scientific_journal-7485	67	27	:	:	PUNCT
american_scientific_journal-7485	67	28	544	544	NUM
american_scientific_journal-7485	67	29	∈	∈	PROPN
american_scientific_journal-7485	67	30	c1	c1	NOUN
american_scientific_journal-7485	67	31	-	-	PUNCT
american_scientific_journal-7485	67	32	e	e	PROPN
american_scientific_journal-7485	67	33	is	be	AUX
american_scientific_journal-7485	67	34	projected	project	VERB
american_scientific_journal-7485	67	35	to	to	ADP
american_scientific_journal-7485	67	36	272	272	NUM
american_scientific_journal-7485	67	37	∈	∈	PROPN
american_scientific_journal-7485	67	38	c2	c2	PROPN
american_scientific_journal-7485	67	39	-	-	PUNCT
american_scientific_journal-7485	67	40	e	e	PROPN
american_scientific_journal-7485	67	41	,	,	PUNCT
american_scientific_journal-7485	67	42			PRON
american_scientific_journal-7485	67	43	(	(	PUNCT
american_scientific_journal-7485	67	44	iii	iii	NOUN
american_scientific_journal-7485	67	45	)	)	PUNCT
american_scientific_journal-7485	67	46	:	:	PUNCT
american_scientific_journal-7485	67	47	34	34	NUM
american_scientific_journal-7485	67	48	∈	∈	PROPN
american_scientific_journal-7485	67	49	c1	c1	NOUN
american_scientific_journal-7485	67	50	-	-	PUNCT
american_scientific_journal-7485	67	51	e	e	PROPN
american_scientific_journal-7485	67	52	is	be	AUX
american_scientific_journal-7485	67	53	projected	project	VERB
american_scientific_journal-7485	67	54	to	to	ADP
american_scientific_journal-7485	67	55	16	16	NUM
american_scientific_journal-7485	67	56	∈	∈	PROPN
american_scientific_journal-7485	67	57	c2	c2	PROPN
american_scientific_journal-7485	67	58	-	-	PUNCT
american_scientific_journal-7485	67	59	o	o	PROPN
american_scientific_journal-7485	67	60	,	,	PUNCT
american_scientific_journal-7485	67	61			PRON
american_scientific_journal-7485	67	62	(	(	PUNCT
american_scientific_journal-7485	67	63	iv	iv	X
american_scientific_journal-7485	67	64	)	)	PUNCT
american_scientific_journal-7485	67	65	:	:	PUNCT
american_scientific_journal-7485	67	66	538	538	NUM
american_scientific_journal-7485	67	67	∈	∈	PROPN
american_scientific_journal-7485	67	68	c1	c1	NOUN
american_scientific_journal-7485	67	69	-	-	PUNCT
american_scientific_journal-7485	67	70	e	e	PROPN
american_scientific_journal-7485	67	71	is	be	AUX
american_scientific_journal-7485	67	72	projected	project	VERB
american_scientific_journal-7485	67	73	to	to	ADP
american_scientific_journal-7485	67	74	269	269	NUM
american_scientific_journal-7485	67	75	∈	∈	PROPN
american_scientific_journal-7485	67	76	c2	c2	PROPN
american_scientific_journal-7485	67	77	-	-	PUNCT
american_scientific_journal-7485	67	78	o.	o.	PROPN
american_scientific_journal-7485	67	79	case	case	NOUN
american_scientific_journal-7485	67	80	4	4	NUM
american_scientific_journal-7485	67	81	:	:	PUNCT
american_scientific_journal-7485	67	82	american	american	ADJ
american_scientific_journal-7485	67	83	academic	academic	ADJ
american_scientific_journal-7485	67	84	scientific	scientific	ADJ
american_scientific_journal-7485	67	85	research	research	NOUN
american_scientific_journal-7485	67	86	journal	journal	NOUN
american_scientific_journal-7485	67	87	for	for	ADP
american_scientific_journal-7485	67	88	engineering	engineering	NOUN
american_scientific_journal-7485	67	89	,	,	PUNCT
american_scientific_journal-7485	67	90	technology	technology	NOUN
american_scientific_journal-7485	67	91	,	,	PUNCT
american_scientific_journal-7485	67	92	and	and	CCONJ
american_scientific_journal-7485	67	93	sciences	science	NOUN
american_scientific_journal-7485	67	94	(	(	PUNCT
american_scientific_journal-7485	67	95	asrjets	asrjet	NOUN
american_scientific_journal-7485	67	96	)	)	PUNCT
american_scientific_journal-7485	67	97	(	(	PUNCT
american_scientific_journal-7485	67	98	2022	2022	NUM
american_scientific_journal-7485	67	99	)	)	PUNCT
american_scientific_journal-7485	67	100	volume	volume	NOUN
american_scientific_journal-7485	67	101	88	88	NUM
american_scientific_journal-7485	67	102	,	,	PUNCT
american_scientific_journal-7485	67	103	no	no	DET
american_scientific_journal-7485	67	104	1	1	NUM
american_scientific_journal-7485	67	105	,	,	PUNCT
american_scientific_journal-7485	67	106	pp	pp	ADV
american_scientific_journal-7485	67	107	91	91	NUM
american_scientific_journal-7485	67	108	-	-	SYM
american_scientific_journal-7485	67	109	98	98	NUM
american_scientific_journal-7485	67	110	96	96	NUM
american_scientific_journal-7485	67	111	every	every	DET
american_scientific_journal-7485	67	112	number	number	NOUN
american_scientific_journal-7485	67	113	of	of	ADP
american_scientific_journal-7485	67	114	c1	c1	NOUN
american_scientific_journal-7485	67	115	-	-	PUNCT
american_scientific_journal-7485	67	116	o	o	PROPN
american_scientific_journal-7485	67	117	subclass	subclass	NOUN
american_scientific_journal-7485	67	118	is	be	AUX
american_scientific_journal-7485	67	119	a	a	DET
american_scientific_journal-7485	67	120	collatz	collatz	NOUN
american_scientific_journal-7485	67	121	projection	projection	NOUN
american_scientific_journal-7485	67	122	to	to	ADP
american_scientific_journal-7485	67	123	numbers	number	NOUN
american_scientific_journal-7485	67	124	of	of	ADP
american_scientific_journal-7485	67	125	c1	c1	NOUN
american_scientific_journal-7485	67	126	-	-	PUNCT
american_scientific_journal-7485	67	127	e	e	NOUN
american_scientific_journal-7485	67	128	subclass	subclass	NOUN
american_scientific_journal-7485	67	129	,	,	PUNCT
american_scientific_journal-7485	67	130	and	and	CCONJ
american_scientific_journal-7485	67	131	it	it	PRON
american_scientific_journal-7485	67	132	takes	take	VERB
american_scientific_journal-7485	67	133	only	only	ADV
american_scientific_journal-7485	67	134	one	one	NUM
american_scientific_journal-7485	67	135	iteration	iteration	NOUN
american_scientific_journal-7485	67	136	.	.	PUNCT
american_scientific_journal-7485	68	1	for	for	ADP
american_scientific_journal-7485	68	2	example	example	NOUN
american_scientific_journal-7485	68	3	:	:	PUNCT
american_scientific_journal-7485	68	4			NOUN
american_scientific_journal-7485	68	5	(	(	PUNCT
american_scientific_journal-7485	68	6	i	i	NOUN
american_scientific_journal-7485	68	7	)	)	PUNCT
american_scientific_journal-7485	68	8	31	31	NUM
american_scientific_journal-7485	68	9	∈	∈	PROPN
american_scientific_journal-7485	68	10	c1	c1	NOUN
american_scientific_journal-7485	68	11	-	-	PUNCT
american_scientific_journal-7485	68	12	o	o	PROPN
american_scientific_journal-7485	68	13	is	be	AUX
american_scientific_journal-7485	68	14	projected	project	VERB
american_scientific_journal-7485	68	15	to	to	ADP
american_scientific_journal-7485	68	16	94	94	NUM
american_scientific_journal-7485	68	17	∈	∈	PROPN
american_scientific_journal-7485	68	18	c1	c1	NOUN
american_scientific_journal-7485	68	19	-	-	PUNCT
american_scientific_journal-7485	68	20	e	e	PROPN
american_scientific_journal-7485	68	21	,	,	PUNCT
american_scientific_journal-7485	68	22			PRON
american_scientific_journal-7485	68	23	(	(	PUNCT
american_scientific_journal-7485	68	24	ii	ii	NOUN
american_scientific_journal-7485	68	25	)	)	PUNCT
american_scientific_journal-7485	68	26	:	:	PUNCT
american_scientific_journal-7485	68	27	223	223	NUM
american_scientific_journal-7485	68	28	∈	∈	PROPN
american_scientific_journal-7485	68	29	c1	c1	PROPN
american_scientific_journal-7485	68	30	-	-	PUNCT
american_scientific_journal-7485	68	31	o	o	PROPN
american_scientific_journal-7485	68	32	projected	project	VERB
american_scientific_journal-7485	68	33	to	to	ADP
american_scientific_journal-7485	68	34	670	670	NUM
american_scientific_journal-7485	68	35	∈	∈	PROPN
american_scientific_journal-7485	68	36	c1	c1	PROPN
american_scientific_journal-7485	68	37	-	-	PUNCT
american_scientific_journal-7485	68	38	e.	e.	PROPN
american_scientific_journal-7485	68	39	moreover	moreover	ADV
american_scientific_journal-7485	68	40	,	,	PUNCT
american_scientific_journal-7485	68	41	we	we	PRON
american_scientific_journal-7485	68	42	see	see	VERB
american_scientific_journal-7485	68	43	that	that	SCONJ
american_scientific_journal-7485	68	44	no	no	DET
american_scientific_journal-7485	68	45	c1	c1	NOUN
american_scientific_journal-7485	68	46	-	-	PUNCT
american_scientific_journal-7485	68	47	e	e	PROPN
american_scientific_journal-7485	68	48	or	or	CCONJ
american_scientific_journal-7485	68	49	c1	c1	PROPN
american_scientific_journal-7485	68	50	-	-	PUNCT
american_scientific_journal-7485	68	51	o	o	NOUN
american_scientific_journal-7485	68	52	number	number	NOUN
american_scientific_journal-7485	68	53	ever	ever	ADV
american_scientific_journal-7485	68	54	projects	project	VERB
american_scientific_journal-7485	68	55	to	to	PART
american_scientific_journal-7485	68	56	become	become	VERB
american_scientific_journal-7485	68	57	a	a	DET
american_scientific_journal-7485	68	58	c3	c3	NOUN
american_scientific_journal-7485	68	59	number	number	NOUN
american_scientific_journal-7485	68	60	.	.	PUNCT
american_scientific_journal-7485	69	1	case	case	NOUN
american_scientific_journal-7485	69	2	5	5	NUM
american_scientific_journal-7485	69	3	:	:	PUNCT
american_scientific_journal-7485	69	4	by	by	ADP
american_scientific_journal-7485	69	5	the	the	DET
american_scientific_journal-7485	69	6	collatz	collatz	NOUN
american_scientific_journal-7485	69	7	conjecture	conjecture	VERB
american_scientific_journal-7485	69	8	,	,	PUNCT
american_scientific_journal-7485	69	9	every	every	DET
american_scientific_journal-7485	69	10	number	number	NOUN
american_scientific_journal-7485	69	11	of	of	ADP
american_scientific_journal-7485	69	12	c2	c2	PROPN
american_scientific_journal-7485	69	13	-	-	PUNCT
american_scientific_journal-7485	69	14	e	e	PROPN
american_scientific_journal-7485	69	15	subclass	subclass	NOUN
american_scientific_journal-7485	69	16	is	be	AUX
american_scientific_journal-7485	69	17	projected	project	VERB
american_scientific_journal-7485	69	18	to	to	ADP
american_scientific_journal-7485	69	19	a	a	DET
american_scientific_journal-7485	69	20	number	number	NOUN
american_scientific_journal-7485	69	21	of	of	ADP
american_scientific_journal-7485	69	22	c1	c1	NOUN
american_scientific_journal-7485	69	23	-	-	PUNCT
american_scientific_journal-7485	69	24	e	e	NOUN
american_scientific_journal-7485	69	25	subclass	subclass	NOUN
american_scientific_journal-7485	69	26	or	or	CCONJ
american_scientific_journal-7485	69	27	to	to	ADP
american_scientific_journal-7485	69	28	a	a	DET
american_scientific_journal-7485	69	29	number	number	NOUN
american_scientific_journal-7485	69	30	of	of	ADP
american_scientific_journal-7485	69	31	c1	c1	NOUN
american_scientific_journal-7485	69	32	-	-	PUNCT
american_scientific_journal-7485	69	33	o	o	PROPN
american_scientific_journal-7485	69	34	subclass	subclass	NOUN
american_scientific_journal-7485	69	35	after	after	ADP
american_scientific_journal-7485	69	36	one	one	NUM
american_scientific_journal-7485	69	37	iteration	iteration	NOUN
american_scientific_journal-7485	69	38	only	only	ADV
american_scientific_journal-7485	69	39	.	.	PUNCT
american_scientific_journal-7485	70	1	for	for	ADP
american_scientific_journal-7485	70	2	example	example	NOUN
american_scientific_journal-7485	70	3	:	:	PUNCT
american_scientific_journal-7485	70	4			NOUN
american_scientific_journal-7485	70	5	(	(	PUNCT
american_scientific_journal-7485	70	6	i	i	NOUN
american_scientific_journal-7485	70	7	)	)	PUNCT
american_scientific_journal-7485	70	8	:	:	PUNCT
american_scientific_journal-7485	70	9	140	140	NUM
american_scientific_journal-7485	70	10	∈	∈	PROPN
american_scientific_journal-7485	70	11	c2	c2	PROPN
american_scientific_journal-7485	70	12	-	-	PUNCT
american_scientific_journal-7485	70	13	e	e	PROPN
american_scientific_journal-7485	70	14	projected	project	VERB
american_scientific_journal-7485	70	15	to	to	ADP
american_scientific_journal-7485	70	16	70	70	NUM
american_scientific_journal-7485	70	17	∈	∈	PROPN
american_scientific_journal-7485	70	18	c1	c1	NOUN
american_scientific_journal-7485	70	19	-	-	PUNCT
american_scientific_journal-7485	70	20	e	e	PROPN
american_scientific_journal-7485	70	21	,	,	PUNCT
american_scientific_journal-7485	70	22			PRON
american_scientific_journal-7485	70	23	(	(	PUNCT
american_scientific_journal-7485	70	24	ii	ii	NOUN
american_scientific_journal-7485	70	25	)	)	PUNCT
american_scientific_journal-7485	70	26	:	:	PUNCT
american_scientific_journal-7485	70	27	788	788	NUM
american_scientific_journal-7485	70	28	∈	∈	PROPN
american_scientific_journal-7485	70	29	c2	c2	PROPN
american_scientific_journal-7485	70	30	-	-	PUNCT
american_scientific_journal-7485	70	31	e	e	PROPN
american_scientific_journal-7485	70	32	projected	project	VERB
american_scientific_journal-7485	70	33	to	to	ADP
american_scientific_journal-7485	70	34	394	394	NUM
american_scientific_journal-7485	70	35	∈	∈	PROPN
american_scientific_journal-7485	70	36	c1	c1	NOUN
american_scientific_journal-7485	70	37	-	-	PUNCT
american_scientific_journal-7485	70	38	e	e	PROPN
american_scientific_journal-7485	70	39	,	,	PUNCT
american_scientific_journal-7485	70	40			PRON
american_scientific_journal-7485	70	41	(	(	PUNCT
american_scientific_journal-7485	70	42	iii	iii	NOUN
american_scientific_journal-7485	70	43	)	)	PUNCT
american_scientific_journal-7485	70	44	:	:	PUNCT
american_scientific_journal-7485	70	45	1478	1478	NUM
american_scientific_journal-7485	70	46	∈	∈	PROPN
american_scientific_journal-7485	70	47	c2	c2	PROPN
american_scientific_journal-7485	70	48	-	-	PUNCT
american_scientific_journal-7485	70	49	e	e	PROPN
american_scientific_journal-7485	70	50	projected	project	VERB
american_scientific_journal-7485	70	51	to	to	ADP
american_scientific_journal-7485	70	52	739	739	NUM
american_scientific_journal-7485	70	53	∈	∈	PROPN
american_scientific_journal-7485	70	54	c1	c1	NOUN
american_scientific_journal-7485	70	55	-	-	PUNCT
american_scientific_journal-7485	70	56	o	o	PROPN
american_scientific_journal-7485	70	57	,	,	PUNCT
american_scientific_journal-7485	70	58			PRON
american_scientific_journal-7485	70	59	(	(	PUNCT
american_scientific_journal-7485	70	60	iv	iv	X
american_scientific_journal-7485	70	61	)	)	PUNCT
american_scientific_journal-7485	70	62	:	:	PUNCT
american_scientific_journal-7485	70	63	146	146	NUM
american_scientific_journal-7485	70	64	∈	∈	PROPN
american_scientific_journal-7485	70	65	c2	c2	PROPN
american_scientific_journal-7485	70	66	-	-	PUNCT
american_scientific_journal-7485	70	67	e	e	PROPN
american_scientific_journal-7485	70	68	projected	project	VERB
american_scientific_journal-7485	70	69	to	to	ADP
american_scientific_journal-7485	70	70	73	73	NUM
american_scientific_journal-7485	70	71	∈	∈	PROPN
american_scientific_journal-7485	70	72	c1	c1	NOUN
american_scientific_journal-7485	70	73	-	-	PUNCT
american_scientific_journal-7485	70	74	o.	o.	PROPN
american_scientific_journal-7485	70	75	case	case	NOUN
american_scientific_journal-7485	70	76	6	6	NUM
american_scientific_journal-7485	70	77	:	:	PUNCT
american_scientific_journal-7485	70	78	using	use	VERB
american_scientific_journal-7485	70	79	the	the	DET
american_scientific_journal-7485	70	80	collatz	collatz	NOUN
american_scientific_journal-7485	70	81	conjecture	conjecture	VERB
american_scientific_journal-7485	70	82	every	every	DET
american_scientific_journal-7485	70	83	number	number	NOUN
american_scientific_journal-7485	70	84	of	of	ADP
american_scientific_journal-7485	70	85	c2	c2	PROPN
american_scientific_journal-7485	70	86	-	-	PUNCT
american_scientific_journal-7485	70	87	o	o	PROPN
american_scientific_journal-7485	70	88	subclass	subclass	NOUN
american_scientific_journal-7485	70	89	is	be	AUX
american_scientific_journal-7485	70	90	projected	project	VERB
american_scientific_journal-7485	70	91	to	to	ADP
american_scientific_journal-7485	70	92	a	a	DET
american_scientific_journal-7485	70	93	number	number	NOUN
american_scientific_journal-7485	70	94	of	of	ADP
american_scientific_journal-7485	70	95	c1	c1	NOUN
american_scientific_journal-7485	70	96	-	-	PUNCT
american_scientific_journal-7485	70	97	e	e	PROPN
american_scientific_journal-7485	70	98	subclass	subclass	NOUN
american_scientific_journal-7485	70	99	after	after	ADP
american_scientific_journal-7485	70	100	one	one	NUM
american_scientific_journal-7485	70	101	iteration	iteration	NOUN
american_scientific_journal-7485	70	102	only	only	ADV
american_scientific_journal-7485	70	103	.	.	PUNCT
american_scientific_journal-7485	71	1	for	for	ADP
american_scientific_journal-7485	71	2	example	example	NOUN
american_scientific_journal-7485	71	3	:	:	PUNCT
american_scientific_journal-7485	71	4			NOUN
american_scientific_journal-7485	71	5	(	(	PUNCT
american_scientific_journal-7485	71	6	i	i	NOUN
american_scientific_journal-7485	71	7	)	)	PUNCT
american_scientific_journal-7485	71	8	:	:	PUNCT
american_scientific_journal-7485	71	9	41	41	NUM
american_scientific_journal-7485	71	10	∈	∈	NOUN
american_scientific_journal-7485	71	11	c2o	c2o	PROPN
american_scientific_journal-7485	71	12	projected	project	VERB
american_scientific_journal-7485	71	13	to	to	ADP
american_scientific_journal-7485	71	14	124	124	NUM
american_scientific_journal-7485	71	15	∈	∈	PROPN
american_scientific_journal-7485	71	16	c1	c1	NOUN
american_scientific_journal-7485	71	17	-	-	PUNCT
american_scientific_journal-7485	71	18	e	e	PROPN
american_scientific_journal-7485	71	19	,	,	PUNCT
american_scientific_journal-7485	71	20			PRON
american_scientific_journal-7485	71	21	(	(	PUNCT
american_scientific_journal-7485	71	22	ii	ii	NOUN
american_scientific_journal-7485	71	23	)	)	PUNCT
american_scientific_journal-7485	71	24	:	:	PUNCT
american_scientific_journal-7485	71	25	143	143	NUM
american_scientific_journal-7485	71	26	∈	∈	PROPN
american_scientific_journal-7485	71	27	c2	c2	PROPN
american_scientific_journal-7485	71	28	-	-	PUNCT
american_scientific_journal-7485	71	29	o	o	PROPN
american_scientific_journal-7485	71	30	projected	project	VERB
american_scientific_journal-7485	71	31	to	to	ADP
american_scientific_journal-7485	71	32	430	430	NUM
american_scientific_journal-7485	71	33	∈	∈	PROPN
american_scientific_journal-7485	71	34	c1	c1	NOUN
american_scientific_journal-7485	71	35	-	-	PUNCT
american_scientific_journal-7485	71	36	e	e	PROPN
american_scientific_journal-7485	71	37	,	,	PUNCT
american_scientific_journal-7485	71	38			PRON
american_scientific_journal-7485	71	39	(	(	PUNCT
american_scientific_journal-7485	71	40	iii	iii	NOUN
american_scientific_journal-7485	71	41	)	)	PUNCT
american_scientific_journal-7485	71	42	:	:	PUNCT
american_scientific_journal-7485	71	43	1067	1067	NUM
american_scientific_journal-7485	71	44	∈	∈	PROPN
american_scientific_journal-7485	71	45	c2	c2	PROPN
american_scientific_journal-7485	71	46	-	-	PUNCT
american_scientific_journal-7485	71	47	o	o	PROPN
american_scientific_journal-7485	71	48	projected	project	VERB
american_scientific_journal-7485	71	49	to	to	ADP
american_scientific_journal-7485	71	50	3202	3202	NUM
american_scientific_journal-7485	71	51	∈	∈	PROPN
american_scientific_journal-7485	71	52	c	c	X
american_scientific_journal-7485	71	53	-	-	PUNCT
american_scientific_journal-7485	71	54	e.	e.	PROPN
american_scientific_journal-7485	71	55			NOUN
american_scientific_journal-7485	72	1	moreover	moreover	ADV
american_scientific_journal-7485	72	2	no	no	DET
american_scientific_journal-7485	72	3	c2	c2	PROPN
american_scientific_journal-7485	72	4	-	-	PUNCT
american_scientific_journal-7485	72	5	e	e	PROPN
american_scientific_journal-7485	72	6	or	or	CCONJ
american_scientific_journal-7485	72	7	c2	c2	PROPN
american_scientific_journal-7485	72	8	-	-	PUNCT
american_scientific_journal-7485	72	9	o	o	PROPN
american_scientific_journal-7485	72	10	number	number	NOUN
american_scientific_journal-7485	72	11	ever	ever	ADV
american_scientific_journal-7485	72	12	projects	project	VERB
american_scientific_journal-7485	72	13	to	to	PART
american_scientific_journal-7485	72	14	become	become	VERB
american_scientific_journal-7485	72	15	a	a	DET
american_scientific_journal-7485	72	16	c3	c3	NOUN
american_scientific_journal-7485	72	17	number	number	NOUN
american_scientific_journal-7485	72	18	.	.	PUNCT
american_scientific_journal-7485	73	1	from	from	ADP
american_scientific_journal-7485	73	2	the	the	DET
american_scientific_journal-7485	73	3	above	above	ADJ
american_scientific_journal-7485	73	4	discussion	discussion	NOUN
american_scientific_journal-7485	73	5	,	,	PUNCT
american_scientific_journal-7485	73	6	we	we	PRON
american_scientific_journal-7485	73	7	can	can	AUX
american_scientific_journal-7485	73	8	easily	easily	ADV
american_scientific_journal-7485	73	9	state	state	VERB
american_scientific_journal-7485	73	10	the	the	DET
american_scientific_journal-7485	73	11	following	follow	VERB
american_scientific_journal-7485	73	12	2.1	2.1	NUM
american_scientific_journal-7485	73	13	.	.	PUNCT
american_scientific_journal-7485	74	1	theorem	theorem	VERB
american_scientific_journal-7485	74	2	the	the	DET
american_scientific_journal-7485	74	3	collatz	collatz	NOUN
american_scientific_journal-7485	74	4	conjecture	conjecture	NOUN
american_scientific_journal-7485	74	5	projects	project	NOUN
american_scientific_journal-7485	74	6	every	every	DET
american_scientific_journal-7485	74	7	number	number	NOUN
american_scientific_journal-7485	74	8	of	of	ADP
american_scientific_journal-7485	74	9	c3	c3	PROPN
american_scientific_journal-7485	74	10	-	-	PUNCT
american_scientific_journal-7485	74	11	e	e	NOUN
american_scientific_journal-7485	74	12	subclass	subclass	NOUN
american_scientific_journal-7485	74	13	to	to	ADP
american_scientific_journal-7485	74	14	a	a	DET
american_scientific_journal-7485	74	15	number	number	NOUN
american_scientific_journal-7485	74	16	in	in	ADP
american_scientific_journal-7485	74	17	c3	c3	PROPN
american_scientific_journal-7485	74	18	-	-	PROPN
american_scientific_journal-7485	74	19	o	o	PROPN
american_scientific_journal-7485	74	20	subclass	subclass	NOUN
american_scientific_journal-7485	74	21	with	with	ADP
american_scientific_journal-7485	74	22	no	no	DET
american_scientific_journal-7485	74	23	return	return	NOUN
american_scientific_journal-7485	74	24	path	path	NOUN
american_scientific_journal-7485	74	25	to	to	ADP
american_scientific_journal-7485	74	26	c3	c3	PROPN
american_scientific_journal-7485	74	27	-	-	PROPN
american_scientific_journal-7485	74	28	e.	e.	PROPN
american_scientific_journal-7485	74	29	also	also	ADV
american_scientific_journal-7485	74	30	every	every	DET
american_scientific_journal-7485	74	31	number	number	NOUN
american_scientific_journal-7485	74	32	of	of	ADP
american_scientific_journal-7485	74	33	c3	c3	PROPN
american_scientific_journal-7485	74	34	-	-	PROPN
american_scientific_journal-7485	74	35	o	o	PROPN
american_scientific_journal-7485	74	36	subclass	subclass	NOUN
american_scientific_journal-7485	74	37	is	be	AUX
american_scientific_journal-7485	74	38	projected	project	VERB
american_scientific_journal-7485	74	39	to	to	ADP
american_scientific_journal-7485	74	40	a	a	DET
american_scientific_journal-7485	74	41	c1	c1	NOUN
american_scientific_journal-7485	74	42	-	-	PUNCT
american_scientific_journal-7485	74	43	e	e	NOUN
american_scientific_journal-7485	74	44	subclass	subclass	NOUN
american_scientific_journal-7485	74	45	after	after	ADP
american_scientific_journal-7485	74	46	one	one	NUM
american_scientific_journal-7485	74	47	iteration	iteration	NOUN
american_scientific_journal-7485	74	48	only	only	ADV
american_scientific_journal-7485	74	49	with	with	ADP
american_scientific_journal-7485	74	50	no	no	DET
american_scientific_journal-7485	74	51	return	return	NOUN
american_scientific_journal-7485	74	52	to	to	ADP
american_scientific_journal-7485	74	53	c3	c3	PROPN
american_scientific_journal-7485	74	54	.	.	PUNCT
american_scientific_journal-7485	75	1	from	from	ADP
american_scientific_journal-7485	75	2	the	the	DET
american_scientific_journal-7485	75	3	above	above	ADJ
american_scientific_journal-7485	75	4	theorem	theorem	NOUN
american_scientific_journal-7485	75	5	,	,	PUNCT
american_scientific_journal-7485	75	6	we	we	PRON
american_scientific_journal-7485	75	7	can	can	AUX
american_scientific_journal-7485	75	8	state	state	VERB
american_scientific_journal-7485	75	9	the	the	DET
american_scientific_journal-7485	75	10	following	follow	VERB
american_scientific_journal-7485	75	11	corollary	corollary	NOUN
american_scientific_journal-7485	75	12	:	:	PUNCT
american_scientific_journal-7485	75	13	2.2.corollary	2.2.corollary	NUM
american_scientific_journal-7485	75	14	the	the	DET
american_scientific_journal-7485	75	15	c3	c3	PROPN
american_scientific_journal-7485	75	16	numbers	number	NOUN
american_scientific_journal-7485	75	17	are	be	AUX
american_scientific_journal-7485	75	18	isolated	isolate	VERB
american_scientific_journal-7485	75	19	outside	outside	ADP
american_scientific_journal-7485	75	20	of	of	ADP
american_scientific_journal-7485	75	21	c3	c3	PROPN
american_scientific_journal-7485	75	22	after	after	ADP
american_scientific_journal-7485	75	23	the	the	DET
american_scientific_journal-7485	75	24	above	above	ADJ
american_scientific_journal-7485	75	25	iterations	iteration	NOUN
american_scientific_journal-7485	75	26	to	to	PART
american_scientific_journal-7485	75	27	receive	receive	VERB
american_scientific_journal-7485	75	28	any	any	DET
american_scientific_journal-7485	75	29	projections	projection	NOUN
american_scientific_journal-7485	75	30	from	from	ADP
american_scientific_journal-7485	75	31	c1	c1	PROPN
american_scientific_journal-7485	75	32	or	or	CCONJ
american_scientific_journal-7485	75	33	c2	c2	PROPN
american_scientific_journal-7485	75	34	.	.	PUNCT
american_scientific_journal-7485	76	1	american	american	ADJ
american_scientific_journal-7485	76	2	academic	academic	ADJ
american_scientific_journal-7485	76	3	scientific	scientific	ADJ
american_scientific_journal-7485	76	4	research	research	NOUN
american_scientific_journal-7485	76	5	journal	journal	NOUN
american_scientific_journal-7485	76	6	for	for	ADP
american_scientific_journal-7485	76	7	engineering	engineering	NOUN
american_scientific_journal-7485	76	8	,	,	PUNCT
american_scientific_journal-7485	76	9	technology	technology	NOUN
american_scientific_journal-7485	76	10	,	,	PUNCT
american_scientific_journal-7485	76	11	and	and	CCONJ
american_scientific_journal-7485	76	12	sciences	science	NOUN
american_scientific_journal-7485	76	13	(	(	PUNCT
american_scientific_journal-7485	76	14	asrjets	asrjet	NOUN
american_scientific_journal-7485	76	15	)	)	PUNCT
american_scientific_journal-7485	76	16	(	(	PUNCT
american_scientific_journal-7485	76	17	2022	2022	NUM
american_scientific_journal-7485	76	18	)	)	PUNCT
american_scientific_journal-7485	76	19	volume	volume	NOUN
american_scientific_journal-7485	76	20	88	88	NUM
american_scientific_journal-7485	76	21	,	,	PUNCT
american_scientific_journal-7485	76	22	no	no	DET
american_scientific_journal-7485	76	23	1	1	NUM
american_scientific_journal-7485	76	24	,	,	PUNCT
american_scientific_journal-7485	76	25	pp	pp	ADV
american_scientific_journal-7485	76	26	91	91	NUM
american_scientific_journal-7485	76	27	-	-	SYM
american_scientific_journal-7485	76	28	98	98	NUM
american_scientific_journal-7485	76	29	97	97	NUM
american_scientific_journal-7485	76	30	2.3	2.3	NUM
american_scientific_journal-7485	76	31	.	.	PUNCT
american_scientific_journal-7485	77	1	theorem	theorem	VERB
american_scientific_journal-7485	77	2	the	the	DET
american_scientific_journal-7485	77	3	collatz	collatz	NOUN
american_scientific_journal-7485	77	4	conjecture	conjecture	NOUN
american_scientific_journal-7485	77	5	projects	project	NOUN
american_scientific_journal-7485	77	6	numbers	number	NOUN
american_scientific_journal-7485	77	7	of	of	ADP
american_scientific_journal-7485	77	8	c1	c1	NOUN
american_scientific_journal-7485	77	9	-	-	PUNCT
american_scientific_journal-7485	77	10	e	e	NOUN
american_scientific_journal-7485	77	11	subclass	subclass	NOUN
american_scientific_journal-7485	77	12	to	to	ADP
american_scientific_journal-7485	77	13	either	either	DET
american_scientific_journal-7485	77	14	numbers	number	NOUN
american_scientific_journal-7485	77	15	of	of	ADP
american_scientific_journal-7485	77	16	c2	c2	PROPN
american_scientific_journal-7485	77	17	-	-	PUNCT
american_scientific_journal-7485	77	18	e	e	NOUN
american_scientific_journal-7485	77	19	subclass	subclass	NOUN
american_scientific_journal-7485	77	20	or	or	CCONJ
american_scientific_journal-7485	77	21	to	to	ADP
american_scientific_journal-7485	77	22	numbers	number	NOUN
american_scientific_journal-7485	77	23	of	of	ADP
american_scientific_journal-7485	77	24	c2	c2	PROPN
american_scientific_journal-7485	77	25	-	-	PUNCT
american_scientific_journal-7485	77	26	o	o	PROPN
american_scientific_journal-7485	77	27	subclass	subclass	NOUN
american_scientific_journal-7485	77	28	after	after	ADP
american_scientific_journal-7485	77	29	one	one	NUM
american_scientific_journal-7485	77	30	iteration	iteration	NOUN
american_scientific_journal-7485	77	31	only	only	ADV
american_scientific_journal-7485	77	32	.	.	PUNCT
american_scientific_journal-7485	78	1	also	also	ADV
american_scientific_journal-7485	78	2	every	every	DET
american_scientific_journal-7485	78	3	number	number	NOUN
american_scientific_journal-7485	78	4	of	of	ADP
american_scientific_journal-7485	78	5	c1	c1	NOUN
american_scientific_journal-7485	78	6	-	-	PUNCT
american_scientific_journal-7485	78	7	o	o	NOUN
american_scientific_journal-7485	78	8	subclass	subclass	NOUN
american_scientific_journal-7485	78	9	projects	project	NOUN
american_scientific_journal-7485	78	10	to	to	PART
american_scientific_journal-7485	78	11	stay	stay	VERB
american_scientific_journal-7485	78	12	in	in	ADP
american_scientific_journal-7485	78	13	c1	c1	PROPN
american_scientific_journal-7485	78	14	to	to	PART
american_scientific_journal-7485	78	15	become	become	VERB
american_scientific_journal-7485	78	16	a	a	DET
american_scientific_journal-7485	78	17	c1	c1	NOUN
american_scientific_journal-7485	78	18	-	-	PUNCT
american_scientific_journal-7485	78	19	e	e	NOUN
american_scientific_journal-7485	78	20	number	number	NOUN
american_scientific_journal-7485	78	21	after	after	ADP
american_scientific_journal-7485	78	22	one	one	NUM
american_scientific_journal-7485	78	23	iteration	iteration	NOUN
american_scientific_journal-7485	78	24	only	only	ADV
american_scientific_journal-7485	78	25	.	.	PUNCT
american_scientific_journal-7485	79	1	and	and	CCONJ
american_scientific_journal-7485	79	2	a	a	DET
american_scientific_journal-7485	79	3	c1	c1	NOUN
american_scientific_journal-7485	79	4	-	-	PUNCT
american_scientific_journal-7485	79	5	e	e	PROPN
american_scientific_journal-7485	79	6	or	or	CCONJ
american_scientific_journal-7485	79	7	c1	c1	PROPN
american_scientific_journal-7485	79	8	-	-	PUNCT
american_scientific_journal-7485	79	9	o	o	NOUN
american_scientific_journal-7485	79	10	number	number	NOUN
american_scientific_journal-7485	79	11	can	can	AUX
american_scientific_journal-7485	79	12	never	never	ADV
american_scientific_journal-7485	79	13	project	project	VERB
american_scientific_journal-7485	79	14	to	to	PART
american_scientific_journal-7485	79	15	become	become	VERB
american_scientific_journal-7485	79	16	a	a	DET
american_scientific_journal-7485	79	17	c3	c3	NOUN
american_scientific_journal-7485	79	18	number	number	NOUN
american_scientific_journal-7485	79	19	.	.	PUNCT
american_scientific_journal-7485	80	1	2.4	2.4	NUM
american_scientific_journal-7485	80	2	.	.	PUNCT
american_scientific_journal-7485	80	3	theorem	theorem	VERB
american_scientific_journal-7485	80	4	the	the	DET
american_scientific_journal-7485	80	5	collatz	collatz	NOUN
american_scientific_journal-7485	80	6	conjecture	conjecture	NOUN
american_scientific_journal-7485	80	7	projects	project	NOUN
american_scientific_journal-7485	80	8	every	every	DET
american_scientific_journal-7485	80	9	number	number	NOUN
american_scientific_journal-7485	80	10	of	of	ADP
american_scientific_journal-7485	80	11	c2	c2	PROPN
american_scientific_journal-7485	80	12	-	-	PUNCT
american_scientific_journal-7485	80	13	e	e	NOUN
american_scientific_journal-7485	80	14	subclass	subclass	NOUN
american_scientific_journal-7485	80	15	to	to	ADP
american_scientific_journal-7485	80	16	a	a	DET
american_scientific_journal-7485	80	17	number	number	NOUN
american_scientific_journal-7485	80	18	of	of	ADP
american_scientific_journal-7485	80	19	c1	c1	NOUN
american_scientific_journal-7485	80	20	-	-	PUNCT
american_scientific_journal-7485	80	21	e	e	NOUN
american_scientific_journal-7485	80	22	subclass	subclass	NOUN
american_scientific_journal-7485	80	23	or	or	CCONJ
american_scientific_journal-7485	80	24	c1	c1	NOUN
american_scientific_journal-7485	80	25	-	-	PUNCT
american_scientific_journal-7485	80	26	o	o	NOUN
american_scientific_journal-7485	80	27	subclass	subclass	NOUN
american_scientific_journal-7485	80	28	after	after	ADP
american_scientific_journal-7485	80	29	one	one	NUM
american_scientific_journal-7485	80	30	iteration	iteration	NOUN
american_scientific_journal-7485	80	31	only	only	ADV
american_scientific_journal-7485	80	32	.	.	PUNCT
american_scientific_journal-7485	81	1	also	also	ADV
american_scientific_journal-7485	81	2	every	every	DET
american_scientific_journal-7485	81	3	number	number	NOUN
american_scientific_journal-7485	81	4	of	of	ADP
american_scientific_journal-7485	81	5	c2	c2	PROPN
american_scientific_journal-7485	81	6	-	-	PUNCT
american_scientific_journal-7485	81	7	o	o	PROPN
american_scientific_journal-7485	81	8	subclass	subclass	NOUN
american_scientific_journal-7485	81	9	is	be	AUX
american_scientific_journal-7485	81	10	projected	project	VERB
american_scientific_journal-7485	81	11	to	to	ADP
american_scientific_journal-7485	81	12	a	a	DET
american_scientific_journal-7485	81	13	number	number	NOUN
american_scientific_journal-7485	81	14	of	of	ADP
american_scientific_journal-7485	81	15	c1	c1	NOUN
american_scientific_journal-7485	81	16	-	-	PUNCT
american_scientific_journal-7485	81	17	e	e	PROPN
american_scientific_journal-7485	81	18	subclass	subclass	NOUN
american_scientific_journal-7485	81	19	after	after	ADP
american_scientific_journal-7485	81	20	one	one	NUM
american_scientific_journal-7485	81	21	iteration	iteration	NOUN
american_scientific_journal-7485	81	22	only	only	ADV
american_scientific_journal-7485	81	23	.	.	PUNCT
american_scientific_journal-7485	82	1	and	and	CCONJ
american_scientific_journal-7485	82	2	a	a	DET
american_scientific_journal-7485	82	3	c2	c2	PROPN
american_scientific_journal-7485	82	4	-	-	PUNCT
american_scientific_journal-7485	82	5	e	e	PROPN
american_scientific_journal-7485	82	6	or	or	CCONJ
american_scientific_journal-7485	82	7	c2	c2	PROPN
american_scientific_journal-7485	82	8	-	-	PUNCT
american_scientific_journal-7485	82	9	o	o	NOUN
american_scientific_journal-7485	82	10	number	number	NOUN
american_scientific_journal-7485	82	11	can	can	AUX
american_scientific_journal-7485	82	12	never	never	ADV
american_scientific_journal-7485	82	13	project	project	VERB
american_scientific_journal-7485	82	14	to	to	PART
american_scientific_journal-7485	82	15	become	become	VERB
american_scientific_journal-7485	82	16	a	a	DET
american_scientific_journal-7485	82	17	c3	c3	NOUN
american_scientific_journal-7485	82	18	number	number	NOUN
american_scientific_journal-7485	82	19	.	.	PUNCT
american_scientific_journal-7485	83	1	from	from	ADP
american_scientific_journal-7485	83	2	the	the	DET
american_scientific_journal-7485	83	3	above	above	ADJ
american_scientific_journal-7485	83	4	case	case	NOUN
american_scientific_journal-7485	83	5	,	,	PUNCT
american_scientific_journal-7485	83	6	we	we	PRON
american_scientific_journal-7485	83	7	can	can	AUX
american_scientific_journal-7485	83	8	easily	easily	ADV
american_scientific_journal-7485	83	9	state	state	VERB
american_scientific_journal-7485	83	10	that	that	SCONJ
american_scientific_journal-7485	83	11	because	because	SCONJ
american_scientific_journal-7485	83	12	of	of	ADP
american_scientific_journal-7485	83	13	the	the	DET
american_scientific_journal-7485	83	14	set	set	NOUN
american_scientific_journal-7485	83	15	properties	property	NOUN
american_scientific_journal-7485	83	16	in	in	ADP
american_scientific_journal-7485	83	17	the	the	DET
american_scientific_journal-7485	83	18	3	3	NUM
american_scientific_journal-7485	83	19	column	column	NOUN
american_scientific_journal-7485	83	20	structure	structure	NOUN
american_scientific_journal-7485	83	21	we	we	PRON
american_scientific_journal-7485	83	22	observe	observe	VERB
american_scientific_journal-7485	83	23	that	that	SCONJ
american_scientific_journal-7485	83	24	:	:	PUNCT
american_scientific_journal-7485	83	25	the	the	DET
american_scientific_journal-7485	83	26	number	number	NOUN
american_scientific_journal-7485	83	27	values	value	NOUN
american_scientific_journal-7485	83	28	of	of	ADP
american_scientific_journal-7485	83	29	c3	c3	PROPN
american_scientific_journal-7485	83	30	are	be	AUX
american_scientific_journal-7485	83	31	after	after	ADP
american_scientific_journal-7485	83	32	a	a	DET
american_scientific_journal-7485	83	33	few	few	ADJ
american_scientific_journal-7485	83	34	iterations	iteration	NOUN
american_scientific_journal-7485	83	35	totally	totally	ADV
american_scientific_journal-7485	83	36	out	out	ADP
american_scientific_journal-7485	83	37	of	of	ADP
american_scientific_journal-7485	83	38	the	the	DET
american_scientific_journal-7485	83	39	projections	projection	NOUN
american_scientific_journal-7485	83	40	by	by	ADP
american_scientific_journal-7485	83	41	being	be	AUX
american_scientific_journal-7485	83	42	projected	project	VERB
american_scientific_journal-7485	83	43	to	to	ADP
american_scientific_journal-7485	83	44	c1	c1	PROPN
american_scientific_journal-7485	83	45	-	-	PUNCT
american_scientific_journal-7485	83	46	e	e	PROPN
american_scientific_journal-7485	83	47	with	with	ADP
american_scientific_journal-7485	83	48	no	no	DET
american_scientific_journal-7485	83	49	return	return	NOUN
american_scientific_journal-7485	83	50	to	to	ADP
american_scientific_journal-7485	83	51	c3	c3	NOUN
american_scientific_journal-7485	83	52	by	by	ADP
american_scientific_journal-7485	83	53	either	either	CCONJ
american_scientific_journal-7485	83	54	c1	c1	PROPN
american_scientific_journal-7485	83	55	or	or	CCONJ
american_scientific_journal-7485	83	56	c2	c2	PROPN
american_scientific_journal-7485	83	57	[	[	PUNCT
american_scientific_journal-7485	83	58	figure	figure	NOUN
american_scientific_journal-7485	83	59	1	1	NUM
american_scientific_journal-7485	83	60	]	]	PUNCT
american_scientific_journal-7485	83	61	.	.	PUNCT
american_scientific_journal-7485	84	1	any	any	DET
american_scientific_journal-7485	84	2	number	number	NOUN
american_scientific_journal-7485	84	3	through	through	ADP
american_scientific_journal-7485	84	4	the	the	DET
american_scientific_journal-7485	84	5	sequence	sequence	NOUN
american_scientific_journal-7485	84	6	of	of	ADP
american_scientific_journal-7485	84	7	the	the	DET
american_scientific_journal-7485	84	8	so	so	ADV
american_scientific_journal-7485	84	9	called	call	VERB
american_scientific_journal-7485	84	10	“	"	PUNCT
american_scientific_journal-7485	84	11	hailstorm	hailstorm	NOUN
american_scientific_journal-7485	84	12	numbers	number	NOUN
american_scientific_journal-7485	84	13	”	"	PUNCT
american_scientific_journal-7485	84	14	chaos	chaos	NOUN
american_scientific_journal-7485	84	15	reach	reach	VERB
american_scientific_journal-7485	84	16	a	a	DET
american_scientific_journal-7485	84	17	final	final	ADJ
american_scientific_journal-7485	84	18	periodic	periodic	ADJ
american_scientific_journal-7485	84	19	orbit	orbit	NOUN
american_scientific_journal-7485	84	20	of	of	ADP
american_scientific_journal-7485	84	21	{	{	PUNCT
american_scientific_journal-7485	84	22	1	1	NUM
american_scientific_journal-7485	84	23	,	,	PUNCT
american_scientific_journal-7485	84	24	4	4	NUM
american_scientific_journal-7485	84	25	,	,	PUNCT
american_scientific_journal-7485	84	26	2	2	NUM
american_scientific_journal-7485	84	27	,	,	PUNCT
american_scientific_journal-7485	84	28	1	1	NUM
american_scientific_journal-7485	84	29	}	}	PUNCT
american_scientific_journal-7485	84	30	.	.	PUNCT
american_scientific_journal-7485	85	1	3	3	X
american_scientific_journal-7485	85	2	.	.	X
american_scientific_journal-7485	85	3	conclusion	conclusion	NOUN
american_scientific_journal-7485	85	4	it	it	PRON
american_scientific_journal-7485	85	5	is	be	AUX
american_scientific_journal-7485	85	6	easy	easy	ADJ
american_scientific_journal-7485	85	7	through	through	ADP
american_scientific_journal-7485	85	8	this	this	DET
american_scientific_journal-7485	85	9	novel	novel	ADJ
american_scientific_journal-7485	85	10	approach	approach	NOUN
american_scientific_journal-7485	85	11	and	and	CCONJ
american_scientific_journal-7485	85	12	its	its	PRON
american_scientific_journal-7485	85	13	observations	observation	NOUN
american_scientific_journal-7485	85	14	that	that	PRON
american_scientific_journal-7485	85	15	proof	proof	NOUN
american_scientific_journal-7485	85	16	of	of	ADP
american_scientific_journal-7485	85	17	the	the	DET
american_scientific_journal-7485	85	18	collatz	collatz	NOUN
american_scientific_journal-7485	85	19	conjecture	conjecture	NOUN
american_scientific_journal-7485	85	20	is	be	AUX
american_scientific_journal-7485	85	21	not	not	PART
american_scientific_journal-7485	85	22	intractable	intractable	ADJ
american_scientific_journal-7485	85	23	as	as	ADP
american_scientific_journal-7485	85	24	thought	think	VERB
american_scientific_journal-7485	85	25	.	.	PUNCT
american_scientific_journal-7485	86	1	studying	study	VERB
american_scientific_journal-7485	86	2	the	the	DET
american_scientific_journal-7485	86	3	projections	projection	NOUN
american_scientific_journal-7485	86	4	and	and	CCONJ
american_scientific_journal-7485	86	5	relationships	relationship	NOUN
american_scientific_journal-7485	86	6	of	of	ADP
american_scientific_journal-7485	86	7	odd	odd	ADJ
american_scientific_journal-7485	86	8	and	and	CCONJ
american_scientific_journal-7485	86	9	even	even	ADV
american_scientific_journal-7485	86	10	numbers	number	NOUN
american_scientific_journal-7485	86	11	in	in	ADP
american_scientific_journal-7485	86	12	figure	figure	NOUN
american_scientific_journal-7485	86	13	1	1	NUM
american_scientific_journal-7485	86	14	and	and	CCONJ
american_scientific_journal-7485	86	15	figure	figure	VERB
american_scientific_journal-7485	86	16	2	2	NUM
american_scientific_journal-7485	86	17	shows	show	VERB
american_scientific_journal-7485	86	18	us	we	PRON
american_scientific_journal-7485	86	19	the	the	DET
american_scientific_journal-7485	86	20	following	follow	VERB
american_scientific_journal-7485	86	21	properties	property	NOUN
american_scientific_journal-7485	86	22	:	:	PUNCT
american_scientific_journal-7485	86	23			X
american_scientific_journal-7485	86	24	all	all	DET
american_scientific_journal-7485	86	25	positive	positive	ADJ
american_scientific_journal-7485	86	26	integers	integer	NOUN
american_scientific_journal-7485	86	27	to	to	PART
american_scientific_journal-7485	86	28	infinity	infinity	VERB
american_scientific_journal-7485	86	29	should	should	AUX
american_scientific_journal-7485	86	30	logically	logically	ADV
american_scientific_journal-7485	86	31	follow	follow	VERB
american_scientific_journal-7485	86	32	the	the	DET
american_scientific_journal-7485	86	33	standard	standard	ADJ
american_scientific_journal-7485	86	34	number	number	NOUN
american_scientific_journal-7485	86	35	counting	counting	NOUN
american_scientific_journal-7485	86	36	sequence	sequence	NOUN
american_scientific_journal-7485	86	37	according	accord	VERB
american_scientific_journal-7485	86	38	to	to	ADP
american_scientific_journal-7485	86	39	the	the	DET
american_scientific_journal-7485	86	40	3	3	NUM
american_scientific_journal-7485	86	41	column	column	NOUN
american_scientific_journal-7485	86	42	structure	structure	NOUN
american_scientific_journal-7485	86	43	in	in	ADP
american_scientific_journal-7485	86	44	figure	figure	NOUN
american_scientific_journal-7485	86	45	1	1	NUM
american_scientific_journal-7485	86	46	.	.	PUNCT
american_scientific_journal-7485	86	47			NOUN
american_scientific_journal-7485	87	1	following	follow	VERB
american_scientific_journal-7485	87	2	the	the	DET
american_scientific_journal-7485	87	3	number	number	NOUN
american_scientific_journal-7485	87	4	counting	counting	NOUN
american_scientific_journal-7485	87	5	sequence	sequence	NOUN
american_scientific_journal-7485	87	6	should	should	AUX
american_scientific_journal-7485	87	7	also	also	ADV
american_scientific_journal-7485	87	8	logically	logically	ADV
american_scientific_journal-7485	87	9	follow	follow	VERB
american_scientific_journal-7485	87	10	the	the	DET
american_scientific_journal-7485	87	11	set	set	NOUN
american_scientific_journal-7485	87	12	projection	projection	NOUN
american_scientific_journal-7485	87	13	sequence	sequence	NOUN
american_scientific_journal-7485	87	14	explained	explain	VERB
american_scientific_journal-7485	87	15	in	in	ADP
american_scientific_journal-7485	87	16	figure	figure	NOUN
american_scientific_journal-7485	87	17	2	2	NUM
american_scientific_journal-7485	87	18	with	with	ADP
american_scientific_journal-7485	87	19	its	its	PRON
american_scientific_journal-7485	87	20	unique	unique	ADJ
american_scientific_journal-7485	87	21	set	set	NOUN
american_scientific_journal-7485	87	22	of	of	ADP
american_scientific_journal-7485	87	23	properties	property	NOUN
american_scientific_journal-7485	87	24	for	for	ADP
american_scientific_journal-7485	87	25	each	each	PRON
american_scientific_journal-7485	87	26	of	of	ADP
american_scientific_journal-7485	87	27	the	the	DET
american_scientific_journal-7485	87	28	columns	column	NOUN
american_scientific_journal-7485	87	29	1	1	NUM
american_scientific_journal-7485	87	30	,	,	PUNCT
american_scientific_journal-7485	87	31	2	2	NUM
american_scientific_journal-7485	87	32	and	and	CCONJ
american_scientific_journal-7485	87	33	3	3	NUM
american_scientific_journal-7485	87	34	.	.	NUM
american_scientific_journal-7485	87	35	figures	figure	NOUN
american_scientific_journal-7485	87	36	1	1	NUM
american_scientific_journal-7485	87	37	and	and	CCONJ
american_scientific_journal-7485	87	38	2	2	NUM
american_scientific_journal-7485	87	39	sets	set	VERB
american_scientific_journal-7485	87	40	the	the	DET
american_scientific_journal-7485	87	41	stage	stage	NOUN
american_scientific_journal-7485	87	42	for	for	ADP
american_scientific_journal-7485	87	43	the	the	DET
american_scientific_journal-7485	87	44	proof	proof	NOUN
american_scientific_journal-7485	87	45	that	that	SCONJ
american_scientific_journal-7485	87	46	the	the	DET
american_scientific_journal-7485	87	47	collatz	collatz	NOUN
american_scientific_journal-7485	87	48	conjectures	conjecture	VERB
american_scientific_journal-7485	87	49	’	'	PUNCT
american_scientific_journal-7485	87	50	projections	projection	NOUN
american_scientific_journal-7485	87	51	are	be	AUX
american_scientific_journal-7485	87	52	now	now	ADV
american_scientific_journal-7485	87	53	better	well	ADV
american_scientific_journal-7485	87	54	understood	understand	VERB
american_scientific_journal-7485	87	55	.	.	PUNCT
american_scientific_journal-7485	88	1			X
american_scientific_journal-7485	88	2	(	(	PUNCT
american_scientific_journal-7485	88	3	i	i	NOUN
american_scientific_journal-7485	88	4	)	)	PUNCT
american_scientific_journal-7485	88	5	every	every	DET
american_scientific_journal-7485	88	6	c3	c3	PROPN
american_scientific_journal-7485	88	7	-	-	PUNCT
american_scientific_journal-7485	88	8	e	e	PROPN
american_scientific_journal-7485	88	9	and	and	CCONJ
american_scientific_journal-7485	88	10	c3	c3	PROPN
american_scientific_journal-7485	88	11	-	-	PROPN
american_scientific_journal-7485	88	12	o	o	NOUN
american_scientific_journal-7485	88	13	number	number	NOUN
american_scientific_journal-7485	88	14	projects	project	NOUN
american_scientific_journal-7485	88	15	to	to	ADP
american_scientific_journal-7485	88	16	a	a	DET
american_scientific_journal-7485	88	17	c1	c1	NOUN
american_scientific_journal-7485	88	18	-	-	PUNCT
american_scientific_journal-7485	88	19	e	e	NOUN
american_scientific_journal-7485	88	20	number	number	NOUN
american_scientific_journal-7485	88	21	after	after	ADP
american_scientific_journal-7485	88	22	one	one	NUM
american_scientific_journal-7485	88	23	or	or	CCONJ
american_scientific_journal-7485	88	24	more	more	ADJ
american_scientific_journal-7485	88	25	iterations	iteration	NOUN
american_scientific_journal-7485	88	26	,	,	PUNCT
american_scientific_journal-7485	88	27	and	and	CCONJ
american_scientific_journal-7485	88	28	that	that	SCONJ
american_scientific_journal-7485	88	29	c3	c3	PROPN
american_scientific_journal-7485	88	30	after	after	SCONJ
american_scientific_journal-7485	88	31	these	these	DET
american_scientific_journal-7485	88	32	iterations	iteration	NOUN
american_scientific_journal-7485	88	33	is	be	AUX
american_scientific_journal-7485	88	34	immune	immune	ADJ
american_scientific_journal-7485	88	35	to	to	PART
american_scientific_journal-7485	88	36	receive	receive	VERB
american_scientific_journal-7485	88	37	any	any	DET
american_scientific_journal-7485	88	38	further	further	ADJ
american_scientific_journal-7485	88	39	projections	projection	NOUN
american_scientific_journal-7485	88	40	from	from	ADP
american_scientific_journal-7485	88	41	c1	c1	PROPN
american_scientific_journal-7485	88	42	,	,	PUNCT
american_scientific_journal-7485	88	43	c2	c2	PROPN
american_scientific_journal-7485	88	44	or	or	CCONJ
american_scientific_journal-7485	88	45	c3	c3	PROPN
american_scientific_journal-7485	88	46	.	.	PUNCT
american_scientific_journal-7485	89	1			X
american_scientific_journal-7485	89	2	(	(	PUNCT
american_scientific_journal-7485	89	3	ii	ii	NOUN
american_scientific_journal-7485	89	4	)	)	PUNCT
american_scientific_journal-7485	89	5	c1	c1	PROPN
american_scientific_journal-7485	89	6	-	-	PUNCT
american_scientific_journal-7485	89	7	o	o	NOUN
american_scientific_journal-7485	89	8	numbers	number	NOUN
american_scientific_journal-7485	89	9	after	after	ADP
american_scientific_journal-7485	89	10	one	one	NUM
american_scientific_journal-7485	89	11	iteration	iteration	NOUN
american_scientific_journal-7485	89	12	project	project	NOUN
american_scientific_journal-7485	89	13	to	to	ADP
american_scientific_journal-7485	89	14	a	a	DET
american_scientific_journal-7485	89	15	higher	high	ADJ
american_scientific_journal-7485	89	16	number	number	NOUN
american_scientific_journal-7485	89	17	in	in	ADP
american_scientific_journal-7485	89	18	c1	c1	NOUN
american_scientific_journal-7485	89	19	-	-	PUNCT
american_scientific_journal-7485	89	20	e	e	NOUN
american_scientific_journal-7485	89	21	if	if	SCONJ
american_scientific_journal-7485	89	22	not	not	PART
american_scientific_journal-7485	89	23	reaching	reach	VERB
american_scientific_journal-7485	89	24	the	the	DET
american_scientific_journal-7485	89	25	value	value	NOUN
american_scientific_journal-7485	89	26	of	of	ADP
american_scientific_journal-7485	89	27	1	1	NUM
american_scientific_journal-7485	89	28	.	.	PUNCT
american_scientific_journal-7485	90	1			PRON
american_scientific_journal-7485	90	2	(	(	PUNCT
american_scientific_journal-7485	90	3	iii	iii	X
american_scientific_journal-7485	90	4	)	)	PUNCT
american_scientific_journal-7485	90	5	c2	c2	PROPN
american_scientific_journal-7485	90	6	-	-	PUNCT
american_scientific_journal-7485	90	7	o	o	NOUN
american_scientific_journal-7485	90	8	numbers	number	NOUN
american_scientific_journal-7485	90	9	after	after	ADP
american_scientific_journal-7485	90	10	one	one	NUM
american_scientific_journal-7485	90	11	iteration	iteration	NOUN
american_scientific_journal-7485	90	12	only	only	ADV
american_scientific_journal-7485	90	13	projects	project	NOUN
american_scientific_journal-7485	90	14	to	to	ADP
american_scientific_journal-7485	90	15	a	a	DET
american_scientific_journal-7485	90	16	higher	high	ADJ
american_scientific_journal-7485	90	17	number	number	NOUN
american_scientific_journal-7485	90	18	in	in	ADP
american_scientific_journal-7485	90	19	c1	c1	PROPN
american_scientific_journal-7485	90	20	-	-	PUNCT
american_scientific_journal-7485	90	21	e.	e.	PROPN
american_scientific_journal-7485	90	22			PROPN
american_scientific_journal-7485	90	23	(	(	PUNCT
american_scientific_journal-7485	90	24	iv	iv	X
american_scientific_journal-7485	90	25	)	)	PUNCT
american_scientific_journal-7485	90	26	c2	c2	PROPN
american_scientific_journal-7485	90	27	-	-	PUNCT
american_scientific_journal-7485	90	28	e	e	NOUN
american_scientific_journal-7485	90	29	numbers	number	NOUN
american_scientific_journal-7485	90	30	after	after	ADP
american_scientific_journal-7485	90	31	one	one	NUM
american_scientific_journal-7485	90	32	iteration	iteration	NOUN
american_scientific_journal-7485	90	33	only	only	ADV
american_scientific_journal-7485	90	34	projects	project	NOUN
american_scientific_journal-7485	90	35	to	to	ADP
american_scientific_journal-7485	90	36	a	a	DET
american_scientific_journal-7485	90	37	lower	low	ADJ
american_scientific_journal-7485	90	38	c1	c1	NOUN
american_scientific_journal-7485	90	39	-	-	PUNCT
american_scientific_journal-7485	90	40	e	e	NOUN
american_scientific_journal-7485	90	41	number	number	NOUN
american_scientific_journal-7485	90	42	.	.	PUNCT
american_scientific_journal-7485	91	1			X
american_scientific_journal-7485	91	2	(	(	PUNCT
american_scientific_journal-7485	91	3	v	v	NOUN
american_scientific_journal-7485	91	4	)	)	PUNCT
american_scientific_journal-7485	91	5	c1	c1	NOUN
american_scientific_journal-7485	91	6	-	-	PUNCT
american_scientific_journal-7485	91	7	e	e	NOUN
american_scientific_journal-7485	91	8	numbers	number	NOUN
american_scientific_journal-7485	91	9	cover	cover	VERB
american_scientific_journal-7485	91	10	the	the	DET
american_scientific_journal-7485	91	11	full	full	ADJ
american_scientific_journal-7485	91	12	sequence	sequence	NOUN
american_scientific_journal-7485	91	13	of	of	ADP
american_scientific_journal-7485	91	14	numbers	number	NOUN
american_scientific_journal-7485	91	15	in	in	ADP
american_scientific_journal-7485	91	16	c2	c2	PROPN
american_scientific_journal-7485	91	17	-	-	PUNCT
american_scientific_journal-7485	91	18	e	e	PROPN
american_scientific_journal-7485	91	19	and	and	CCONJ
american_scientific_journal-7485	91	20	c2	c2	PROPN
american_scientific_journal-7485	91	21	-	-	PUNCT
american_scientific_journal-7485	91	22	o	o	PROPN
american_scientific_journal-7485	91	23	,	,	PUNCT
american_scientific_journal-7485	91	24	for	for	ADP
american_scientific_journal-7485	91	25	example	example	NOUN
american_scientific_journal-7485	91	26	:	:	PUNCT
american_scientific_journal-7485	91	27	c1	c1	NOUN
american_scientific_journal-7485	91	28	-	-	PUNCT
american_scientific_journal-7485	91	29	e	e	PROPN
american_scientific_journal-7485	91	30	(	(	PUNCT
american_scientific_journal-7485	91	31	4	4	NUM
american_scientific_journal-7485	91	32	)	)	PUNCT
american_scientific_journal-7485	91	33	to	to	ADP
american_scientific_journal-7485	91	34	c2	c2	PROPN
american_scientific_journal-7485	91	35	-	-	PUNCT
american_scientific_journal-7485	91	36	e	e	PROPN
american_scientific_journal-7485	91	37	(	(	PUNCT
american_scientific_journal-7485	91	38	2	2	NUM
american_scientific_journal-7485	91	39	)	)	PUNCT
american_scientific_journal-7485	91	40	;	;	PUNCT
american_scientific_journal-7485	91	41	c1	c1	PROPN
american_scientific_journal-7485	91	42	-	-	PUNCT
american_scientific_journal-7485	91	43	e	e	PROPN
american_scientific_journal-7485	91	44	(	(	PUNCT
american_scientific_journal-7485	91	45	10	10	NUM
american_scientific_journal-7485	91	46	)	)	PUNCT
american_scientific_journal-7485	91	47	to	to	ADP
american_scientific_journal-7485	91	48	c2	c2	PROPN
american_scientific_journal-7485	91	49	-	-	PUNCT
american_scientific_journal-7485	91	50	o	o	PROPN
american_scientific_journal-7485	91	51	(	(	PUNCT
american_scientific_journal-7485	91	52	5	5	NUM
american_scientific_journal-7485	91	53	)	)	PUNCT
american_scientific_journal-7485	91	54	;	;	PUNCT
american_scientific_journal-7485	91	55	c1	c1	PROPN
american_scientific_journal-7485	91	56	-	-	PUNCT
american_scientific_journal-7485	91	57	e	e	PROPN
american_scientific_journal-7485	91	58	(	(	PUNCT
american_scientific_journal-7485	91	59	16	16	NUM
american_scientific_journal-7485	91	60	)	)	PUNCT
american_scientific_journal-7485	91	61	to	to	ADP
american_scientific_journal-7485	91	62	c2	c2	PROPN
american_scientific_journal-7485	91	63	-	-	PUNCT
american_scientific_journal-7485	91	64	o	o	PROPN
american_scientific_journal-7485	91	65	(	(	PUNCT
american_scientific_journal-7485	91	66	8)	8)	NUM
american_scientific_journal-7485	91	67	;	;	PUNCT
american_scientific_journal-7485	91	68	c1	c1	NOUN
american_scientific_journal-7485	91	69	-	-	PUNCT
american_scientific_journal-7485	91	70	e	e	PROPN
american_scientific_journal-7485	91	71	(	(	PUNCT
american_scientific_journal-7485	91	72	22	22	NUM
american_scientific_journal-7485	91	73	)	)	PUNCT
american_scientific_journal-7485	91	74	to	to	ADP
american_scientific_journal-7485	91	75	c2	c2	PROPN
american_scientific_journal-7485	91	76	-	-	PUNCT
american_scientific_journal-7485	91	77	o	o	PROPN
american_scientific_journal-7485	91	78	(	(	PUNCT
american_scientific_journal-7485	91	79	11	11	NUM
american_scientific_journal-7485	91	80	)	)	PUNCT
american_scientific_journal-7485	91	81	etc	etc	X
american_scientific_journal-7485	91	82	.	.	X
american_scientific_journal-7485	91	83	,	,	PUNCT
american_scientific_journal-7485	91	84			X
american_scientific_journal-7485	91	85	(	(	PUNCT
american_scientific_journal-7485	91	86	vi	vi	NOUN
american_scientific_journal-7485	91	87	)	)	PUNCT
american_scientific_journal-7485	91	88	c1	c1	NOUN
american_scientific_journal-7485	91	89	-	-	PUNCT
american_scientific_journal-7485	91	90	o	o	NOUN
american_scientific_journal-7485	91	91	numbers	number	NOUN
american_scientific_journal-7485	91	92	projects	project	NOUN
american_scientific_journal-7485	91	93	to	to	ADP
american_scientific_journal-7485	91	94	c1	c1	NOUN
american_scientific_journal-7485	91	95	-	-	PUNCT
american_scientific_journal-7485	91	96	e	e	PROPN
american_scientific_journal-7485	91	97	to	to	PART
american_scientific_journal-7485	91	98	cover	cover	VERB
american_scientific_journal-7485	91	99	the	the	DET
american_scientific_journal-7485	91	100	sequence	sequence	NOUN
american_scientific_journal-7485	91	101	again	again	ADV
american_scientific_journal-7485	91	102	in	in	ADP
american_scientific_journal-7485	91	103	(	(	PUNCT
american_scientific_journal-7485	91	104	v	v	NOUN
american_scientific_journal-7485	91	105	)	)	PUNCT
american_scientific_journal-7485	91	106	,	,	PUNCT
american_scientific_journal-7485	91	107	for	for	ADP
american_scientific_journal-7485	91	108	example	example	NOUN
american_scientific_journal-7485	91	109	:	:	PUNCT
american_scientific_journal-7485	91	110	c1	c1	PROPN
american_scientific_journal-7485	91	111	-	-	PUNCT
american_scientific_journal-7485	91	112	o	o	PROPN
american_scientific_journal-7485	91	113	(	(	PUNCT
american_scientific_journal-7485	91	114	7	7	NUM
american_scientific_journal-7485	91	115	)	)	PUNCT
american_scientific_journal-7485	91	116	to	to	ADP
american_scientific_journal-7485	91	117	c1	c1	PROPN
american_scientific_journal-7485	91	118	-	-	PUNCT
american_scientific_journal-7485	91	119	e	e	PROPN
american_scientific_journal-7485	91	120	(	(	PUNCT
american_scientific_journal-7485	91	121	22	22	NUM
american_scientific_journal-7485	91	122	)	)	PUNCT
american_scientific_journal-7485	91	123	;	;	PUNCT
american_scientific_journal-7485	91	124	c1	c1	PROPN
american_scientific_journal-7485	91	125	-	-	PUNCT
american_scientific_journal-7485	91	126	o	o	PROPN
american_scientific_journal-7485	91	127	(	(	PUNCT
american_scientific_journal-7485	91	128	13	13	NUM
american_scientific_journal-7485	91	129	)	)	PUNCT
american_scientific_journal-7485	91	130	to	to	ADP
american_scientific_journal-7485	91	131	c1	c1	PROPN
american_scientific_journal-7485	91	132	-	-	PUNCT
american_scientific_journal-7485	91	133	e	e	PROPN
american_scientific_journal-7485	91	134	(	(	PUNCT
american_scientific_journal-7485	91	135	40	40	NUM
american_scientific_journal-7485	91	136	)	)	PUNCT
american_scientific_journal-7485	91	137	.	.	PUNCT
american_scientific_journal-7485	92	1	this	this	DET
american_scientific_journal-7485	92	2	process	process	NOUN
american_scientific_journal-7485	92	3	reaching	reach	VERB
american_scientific_journal-7485	92	4	a	a	DET
american_scientific_journal-7485	92	5	certain	certain	ADJ
american_scientific_journal-7485	92	6	value	value	NOUN
american_scientific_journal-7485	92	7	such	such	ADJ
american_scientific_journal-7485	92	8	as	as	ADP
american_scientific_journal-7485	92	9	10	10	NUM
american_scientific_journal-7485	92	10	and	and	CCONJ
american_scientific_journal-7485	92	11	64	64	NUM
american_scientific_journal-7485	92	12	open	open	VERB
american_scientific_journal-7485	92	13	the	the	DET
american_scientific_journal-7485	92	14	gates	gate	NOUN
american_scientific_journal-7485	92	15	which	which	PRON
american_scientific_journal-7485	92	16	would	would	AUX
american_scientific_journal-7485	92	17	finally	finally	ADV
american_scientific_journal-7485	92	18	project	project	VERB
american_scientific_journal-7485	92	19	to	to	PART
american_scientific_journal-7485	92	20	attain	attain	VERB
american_scientific_journal-7485	92	21	the	the	DET
american_scientific_journal-7485	92	22	value	value	NOUN
american_scientific_journal-7485	92	23	of	of	ADP
american_scientific_journal-7485	92	24	1	1	NUM
american_scientific_journal-7485	92	25	in	in	ADP
american_scientific_journal-7485	92	26	c1	c1	PROPN
american_scientific_journal-7485	92	27	-	-	PUNCT
american_scientific_journal-7485	92	28	o.	o.	PROPN
american_scientific_journal-7485	92	29	american	american	PROPN
american_scientific_journal-7485	92	30	academic	academic	PROPN
american_scientific_journal-7485	92	31	scientific	scientific	ADJ
american_scientific_journal-7485	92	32	research	research	NOUN
american_scientific_journal-7485	92	33	journal	journal	NOUN
american_scientific_journal-7485	92	34	for	for	ADP
american_scientific_journal-7485	92	35	engineering	engineering	NOUN
american_scientific_journal-7485	92	36	,	,	PUNCT
american_scientific_journal-7485	92	37	technology	technology	NOUN
american_scientific_journal-7485	92	38	,	,	PUNCT
american_scientific_journal-7485	92	39	and	and	CCONJ
american_scientific_journal-7485	92	40	sciences	science	NOUN
american_scientific_journal-7485	92	41	(	(	PUNCT
american_scientific_journal-7485	92	42	asrjets	asrjet	NOUN
american_scientific_journal-7485	92	43	)	)	PUNCT
american_scientific_journal-7485	92	44	(	(	PUNCT
american_scientific_journal-7485	92	45	2022	2022	NUM
american_scientific_journal-7485	92	46	)	)	PUNCT
american_scientific_journal-7485	92	47	volume	volume	NOUN
american_scientific_journal-7485	92	48	88	88	NUM
american_scientific_journal-7485	92	49	,	,	PUNCT
american_scientific_journal-7485	92	50	no	no	DET
american_scientific_journal-7485	92	51	1	1	NUM
american_scientific_journal-7485	92	52	,	,	PUNCT
american_scientific_journal-7485	92	53	pp	pp	ADV
american_scientific_journal-7485	92	54	91	91	NUM
american_scientific_journal-7485	92	55	-	-	SYM
american_scientific_journal-7485	92	56	98	98	NUM
american_scientific_journal-7485	92	57	98	98	NUM
american_scientific_journal-7485	92	58			NOUN
american_scientific_journal-7485	92	59	(	(	PUNCT
american_scientific_journal-7485	92	60	vii	vii	PROPN
american_scientific_journal-7485	92	61	)	)	PUNCT
american_scientific_journal-7485	92	62	a	a	DET
american_scientific_journal-7485	92	63	c2	c2	PROPN
american_scientific_journal-7485	92	64	-	-	PUNCT
american_scientific_journal-7485	92	65	e	e	PROPN
american_scientific_journal-7485	92	66	could	could	AUX
american_scientific_journal-7485	92	67	project	project	VERB
american_scientific_journal-7485	92	68	back	back	ADV
american_scientific_journal-7485	92	69	to	to	ADP
american_scientific_journal-7485	92	70	a	a	DET
american_scientific_journal-7485	92	71	c1	c1	NOUN
american_scientific_journal-7485	92	72	-	-	PUNCT
american_scientific_journal-7485	92	73	e	e	PROPN
american_scientific_journal-7485	92	74	for	for	ADP
american_scientific_journal-7485	92	75	another	another	DET
american_scientific_journal-7485	92	76	operational	operational	ADJ
american_scientific_journal-7485	92	77	repeat	repeat	NOUN
american_scientific_journal-7485	92	78	.	.	PUNCT
american_scientific_journal-7485	93	1	this	this	DET
american_scientific_journal-7485	93	2	approach	approach	NOUN
american_scientific_journal-7485	93	3	indicates	indicate	VERB
american_scientific_journal-7485	93	4	that	that	SCONJ
american_scientific_journal-7485	93	5	the	the	DET
american_scientific_journal-7485	93	6	collatz	collatz	NOUN
american_scientific_journal-7485	93	7	projections	projection	NOUN
american_scientific_journal-7485	93	8	of	of	ADP
american_scientific_journal-7485	93	9	any	any	DET
american_scientific_journal-7485	93	10	starting	starting	NOUN
american_scientific_journal-7485	93	11	number	number	NOUN
american_scientific_journal-7485	93	12	are	be	AUX
american_scientific_journal-7485	93	13	bounded	bound	VERB
american_scientific_journal-7485	93	14	to	to	ADP
american_scientific_journal-7485	93	15	a	a	DET
american_scientific_journal-7485	93	16	set	set	ADJ
american_scientific_journal-7485	93	17	rule	rule	NOUN
american_scientific_journal-7485	93	18	of	of	ADP
american_scientific_journal-7485	93	19	projections	projection	NOUN
american_scientific_journal-7485	93	20	in	in	ADP
american_scientific_journal-7485	93	21	each	each	PRON
american_scientific_journal-7485	93	22	of	of	ADP
american_scientific_journal-7485	93	23	the	the	DET
american_scientific_journal-7485	93	24	3	3	NUM
american_scientific_journal-7485	93	25	columns	column	NOUN
american_scientific_journal-7485	93	26	as	as	SCONJ
american_scientific_journal-7485	93	27	set	set	VERB
american_scientific_journal-7485	93	28	out	out	ADP
american_scientific_journal-7485	93	29	in	in	ADP
american_scientific_journal-7485	93	30	figure	figure	NOUN
american_scientific_journal-7485	93	31	2	2	NUM
american_scientific_journal-7485	93	32	,	,	PUNCT
american_scientific_journal-7485	93	33	with	with	ADP
american_scientific_journal-7485	93	34	c1	c1	NOUN
american_scientific_journal-7485	93	35	-	-	PUNCT
american_scientific_journal-7485	93	36	e	e	NOUN
american_scientific_journal-7485	93	37	the	the	DET
american_scientific_journal-7485	93	38	heart	heart	NOUN
american_scientific_journal-7485	93	39	of	of	ADP
american_scientific_journal-7485	93	40	“	"	PUNCT
american_scientific_journal-7485	93	41	the	the	DET
american_scientific_journal-7485	93	42	hailstorm	hailstorm	NOUN
american_scientific_journal-7485	93	43	”	"	PUNCT
american_scientific_journal-7485	93	44	.	.	PUNCT
american_scientific_journal-7485	94	1	sub	sub	ADJ
american_scientific_journal-7485	94	2	-	-	ADJ
american_scientific_journal-7485	94	3	class	class	ADJ
american_scientific_journal-7485	94	4	c1e	c1e	NOUN
american_scientific_journal-7485	94	5	has	have	VERB
american_scientific_journal-7485	94	6	the	the	DET
american_scientific_journal-7485	94	7	property	property	NOUN
american_scientific_journal-7485	94	8	as	as	ADP
american_scientific_journal-7485	94	9	the	the	DET
american_scientific_journal-7485	94	10	only	only	ADJ
american_scientific_journal-7485	94	11	sub	sub	NOUN
american_scientific_journal-7485	94	12	-	-	NOUN
american_scientific_journal-7485	94	13	class	class	NOUN
american_scientific_journal-7485	94	14	to	to	PART
american_scientific_journal-7485	94	15	receive	receive	VERB
american_scientific_journal-7485	94	16	projections	projection	NOUN
american_scientific_journal-7485	94	17	from	from	ADP
american_scientific_journal-7485	94	18	all	all	DET
american_scientific_journal-7485	94	19	the	the	DET
american_scientific_journal-7485	94	20	other	other	ADJ
american_scientific_journal-7485	94	21	sub	sub	NOUN
american_scientific_journal-7485	94	22	-	-	NOUN
american_scientific_journal-7485	94	23	classes	class	NOUN
american_scientific_journal-7485	94	24	and	and	CCONJ
american_scientific_journal-7485	94	25	projecting	project	VERB
american_scientific_journal-7485	94	26	them	they	PRON
american_scientific_journal-7485	94	27	from	from	ADP
american_scientific_journal-7485	94	28	c1	c1	NOUN
american_scientific_journal-7485	94	29	-	-	PUNCT
american_scientific_journal-7485	94	30	e	e	NOUN
american_scientific_journal-7485	94	31	to	to	PART
american_scientific_journal-7485	94	32	exit	exit	VERB
american_scientific_journal-7485	94	33	through	through	ADP
american_scientific_journal-7485	94	34	c2	c2	PROPN
american_scientific_journal-7485	94	35	-	-	PUNCT
american_scientific_journal-7485	94	36	e	e	PROPN
american_scientific_journal-7485	94	37	to	to	ADP
american_scientific_journal-7485	94	38	c1	c1	PROPN
american_scientific_journal-7485	94	39	-	-	PUNCT
american_scientific_journal-7485	94	40	o	o	PROPN
american_scientific_journal-7485	94	41	value	value	NOUN
american_scientific_journal-7485	94	42	1	1	NUM
american_scientific_journal-7485	94	43	.	.	PUNCT
american_scientific_journal-7485	95	1	acknowledgements	acknowledgement	NOUN
american_scientific_journal-7485	95	2	i	i	PRON
american_scientific_journal-7485	95	3	herewith	herewith	VERB
american_scientific_journal-7485	95	4	express	express	VERB
american_scientific_journal-7485	95	5	my	my	PRON
american_scientific_journal-7485	95	6	gratitude	gratitude	NOUN
american_scientific_journal-7485	95	7	to	to	ADP
american_scientific_journal-7485	95	8	everyone	everyone	PRON
american_scientific_journal-7485	95	9	who	who	PRON
american_scientific_journal-7485	95	10	endured	endure	VERB
american_scientific_journal-7485	95	11	me	i	PRON
american_scientific_journal-7485	95	12	whilst	whilst	SCONJ
american_scientific_journal-7485	95	13	working	work	VERB
american_scientific_journal-7485	95	14	on	on	ADP
american_scientific_journal-7485	95	15	the	the	DET
american_scientific_journal-7485	95	16	conjecture	conjecture	NOUN
american_scientific_journal-7485	95	17	and	and	CCONJ
american_scientific_journal-7485	95	18	the	the	DET
american_scientific_journal-7485	95	19	various	various	ADJ
american_scientific_journal-7485	95	20	inputs	input	NOUN
american_scientific_journal-7485	95	21	of	of	ADP
american_scientific_journal-7485	95	22	dr	dr	PROPN
american_scientific_journal-7485	95	23	.	.	PROPN
american_scientific_journal-7485	95	24	mohamnd	mohamnd	PROPN
american_scientific_journal-7485	95	25	saleem	saleem	PROPN
american_scientific_journal-7485	95	26	lone	lone	ADJ
american_scientific_journal-7485	95	27	.	.	PUNCT
american_scientific_journal-7485	96	1	4	4	X
american_scientific_journal-7485	96	2	.	.	X
american_scientific_journal-7485	96	3	conflict	conflict	NOUN
american_scientific_journal-7485	96	4	of	of	ADP
american_scientific_journal-7485	96	5	interest	interest	NOUN
american_scientific_journal-7485	96	6	statement	statement	NOUN
american_scientific_journal-7485	96	7	the	the	DET
american_scientific_journal-7485	96	8	author	author	NOUN
american_scientific_journal-7485	96	9	declares	declare	VERB
american_scientific_journal-7485	96	10	that	that	SCONJ
american_scientific_journal-7485	96	11	there	there	PRON
american_scientific_journal-7485	96	12	is	be	VERB
american_scientific_journal-7485	96	13	no	no	DET
american_scientific_journal-7485	96	14	conflict	conflict	NOUN
american_scientific_journal-7485	96	15	of	of	ADP
american_scientific_journal-7485	96	16	interest	interest	NOUN
american_scientific_journal-7485	96	17	in	in	ADP
american_scientific_journal-7485	96	18	this	this	DET
american_scientific_journal-7485	96	19	paper	paper	NOUN
american_scientific_journal-7485	96	20	.	.	PUNCT
american_scientific_journal-7485	97	1	the	the	DET
american_scientific_journal-7485	97	2	author	author	NOUN
american_scientific_journal-7485	97	3	declare	declare	VERB
american_scientific_journal-7485	97	4	that	that	SCONJ
american_scientific_journal-7485	97	5	there	there	PRON
american_scientific_journal-7485	97	6	are	be	VERB
american_scientific_journal-7485	97	7	no	no	DET
american_scientific_journal-7485	97	8	other	other	ADJ
american_scientific_journal-7485	97	9	financial	financial	ADJ
american_scientific_journal-7485	97	10	relationships	relationship	NOUN
american_scientific_journal-7485	97	11	with	with	ADP
american_scientific_journal-7485	97	12	any	any	DET
american_scientific_journal-7485	97	13	organizations	organization	NOUN
american_scientific_journal-7485	97	14	that	that	PRON
american_scientific_journal-7485	97	15	might	might	AUX
american_scientific_journal-7485	97	16	have	have	VERB
american_scientific_journal-7485	97	17	an	an	DET
american_scientific_journal-7485	97	18	interest	interest	NOUN
american_scientific_journal-7485	97	19	in	in	ADP
american_scientific_journal-7485	97	20	the	the	DET
american_scientific_journal-7485	97	21	submitted	submit	VERB
american_scientific_journal-7485	97	22	work	work	NOUN
american_scientific_journal-7485	97	23	.	.	PUNCT
american_scientific_journal-7485	98	1	references	reference	NOUN
american_scientific_journal-7485	98	2	[	[	X
american_scientific_journal-7485	98	3	1	1	NUM
american_scientific_journal-7485	98	4	]	]	X
american_scientific_journal-7485	98	5	c.a	c.a	PROPN
american_scientific_journal-7485	98	6	.	.	PROPN
american_scientific_journal-7485	98	7	pickover	pickover	PROPN
american_scientific_journal-7485	98	8	.	.	PUNCT
american_scientific_journal-7485	98	9	”	"	PUNCT
american_scientific_journal-7485	99	1	hailstorm	hailstorm	NOUN
american_scientific_journal-7485	99	2	numbers	number	NOUN
american_scientific_journal-7485	99	3	”	"	PUNCT
american_scientific_journal-7485	99	4	wonders	wonder	NOUN
american_scientific_journal-7485	99	5	of	of	ADP
american_scientific_journal-7485	99	6	numbers	number	NOUN
american_scientific_journal-7485	99	7	,	,	PUNCT
american_scientific_journal-7485	99	8	adventures	adventure	NOUN
american_scientific_journal-7485	99	9	in	in	ADP
american_scientific_journal-7485	99	10	mathematics	mathematic	NOUN
american_scientific_journal-7485	99	11	,	,	PUNCT
american_scientific_journal-7485	99	12	mind	mind	NOUN
american_scientific_journal-7485	99	13	,	,	PUNCT
american_scientific_journal-7485	99	14	and	and	CCONJ
american_scientific_journal-7485	99	15	meaning	meaning	NOUN
american_scientific_journal-7485	99	16	.	.	PUNCT
american_scientific_journal-7485	100	1	oxford	oxford	PROPN
american_scientific_journal-7485	100	2	england	england	PROPN
american_scientific_journal-7485	100	3	:	:	PUNCT
american_scientific_journal-7485	100	4	oxford	oxford	PROPN
american_scientific_journal-7485	100	5	university	university	PROPN
american_scientific_journal-7485	100	6	press	press	NOUN
american_scientific_journal-7485	100	7	,	,	PUNCT
american_scientific_journal-7485	100	8	2001	2001	NUM
american_scientific_journal-7485	100	9	,	,	PUNCT
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american_scientific_journal-7485	100	11	.	.	PUNCT
american_scientific_journal-7485	101	1	116	116	NUM
american_scientific_journal-7485	101	2	–	–	PUNCT
american_scientific_journal-7485	101	3	118	118	NUM
american_scientific_journal-7485	101	4	.	.	PUNCT
american_scientific_journal-7485	102	1	[	[	X
american_scientific_journal-7485	102	2	2	2	NUM
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american_scientific_journal-7485	102	4	j.c	j.c	PROPN
american_scientific_journal-7485	102	5	.	.	PROPN
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american_scientific_journal-7485	102	7	.	.	PUNCT
american_scientific_journal-7485	103	1	the	the	DET
american_scientific_journal-7485	103	2	ultimate	ultimate	ADJ
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american_scientific_journal-7485	103	4	:	:	PUNCT
american_scientific_journal-7485	103	5	the	the	DET
american_scientific_journal-7485	103	6	3x	3x	NUM
american_scientific_journal-7485	103	7	+	+	SYM
american_scientific_journal-7485	103	8	1	1	NUM
american_scientific_journal-7485	103	9	problem	problem	NOUN
american_scientific_journal-7485	103	10	.	.	PUNCT
american_scientific_journal-7485	104	1	american	american	PROPN
american_scientific_journal-7485	104	2	mathematical	mathematical	PROPN
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american_scientific_journal-7485	104	4	,	,	PUNCT
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american_scientific_journal-7485	104	6	.	.	PUNCT
american_scientific_journal-7485	105	1	[	[	X
american_scientific_journal-7485	105	2	3	3	X
american_scientific_journal-7485	105	3	]	]	X
american_scientific_journal-7485	105	4	terrance	terrance	PROPN
american_scientific_journal-7485	105	5	tau	tau	PROPN
american_scientific_journal-7485	105	6	.	.	PUNCT
american_scientific_journal-7485	106	1	“	"	PUNCT
american_scientific_journal-7485	106	2	the	the	DET
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american_scientific_journal-7485	106	4	collatz	collatz	NOUN
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american_scientific_journal-7485	106	6	-	-	PUNCT
american_scientific_journal-7485	106	7	terence	terence	NOUN
american_scientific_journal-7485	106	8	tau	tau	PROPN
american_scientific_journal-7485	106	9	.	.	PUNCT
american_scientific_journal-7485	106	10	”	"	PUNCT
american_scientific_journal-7485	107	1	“	"	PUNCT
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american_scientific_journal-7485	107	12	.	.	PUNCT
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american_scientific_journal-7485	108	2	:	:	PUNCT
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american_scientific_journal-7485	108	4	,	,	PUNCT
american_scientific_journal-7485	108	5	oct	oct	PROPN
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american_scientific_journal-7485	108	7	30	30	NUM
american_scientific_journal-7485	108	8	,	,	PUNCT
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american_scientific_journal-7485	109	1	[	[	X
american_scientific_journal-7485	109	2	jan	jan	PROPN
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american_scientific_journal-7485	109	4	29	29	NUM
american_scientific_journal-7485	109	5	,	,	PUNCT
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american_scientific_journal-7485	109	8	.	.	PUNCT
american_scientific_journal-7485	110	1	[	[	X
american_scientific_journal-7485	110	2	4	4	NUM
american_scientific_journal-7485	110	3	]	]	X
american_scientific_journal-7485	110	4	richard	richard	PROPN
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american_scientific_journal-7485	110	6	.	.	PUNCT
american_scientific_journal-7485	111	1	“	"	PUNCT
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american_scientific_journal-7485	111	4	.	.	PUNCT
american_scientific_journal-7485	112	1	unsolved	unsolved	ADJ
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american_scientific_journal-7485	112	6	.	.	PUNCT
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american_scientific_journal-7485	113	2	-	-	PUNCT
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american_scientific_journal-7485	113	4	,	,	PUNCT
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american_scientific_journal-7485	113	6	,	,	PUNCT
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american_scientific_journal-7485	113	8	336–7	336–7	NUM
american_scientific_journal-7485	113	9	.	.	PUNCT
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american_scientific_journal-7485	114	2	0	0	NUM
american_scientific_journal-7485	114	3	-	-	SYM
american_scientific_journal-7485	114	4	387	387	NUM
american_scientific_journal-7485	114	5	-	-	PUNCT
american_scientific_journal-7485	114	6	20860	20860	NUM
american_scientific_journal-7485	114	7	-	-	SYM
american_scientific_journal-7485	114	8	7	7	NUM
american_scientific_journal-7485	114	9	.	.	PUNCT
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american_scientific_journal-7485	114	11	1058.11001	1058.11001	NUM
american_scientific_journal-7485	114	12	,	,	PUNCT
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american_scientific_journal-7485	115	5	,	,	PUNCT
american_scientific_journal-7485	115	6	a	a	DET
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american_scientific_journal-7485	115	9	,	,	PUNCT
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american_scientific_journal-7485	115	11	.	.	PUNCT
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american_scientific_journal-7485	116	7	.	.	PUNCT
american_scientific_journal-7485	117	1	“	"	PUNCT
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american_scientific_journal-7485	117	4	the	the	DET
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american_scientific_journal-7485	117	8	sliding	slide	VERB
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american_scientific_journal-7485	117	11	.	.	PUNCT
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american_scientific_journal-7485	118	9	-	-	PUNCT
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american_scientific_journal-7485	118	11	.	.	PUNCT
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