id	sid	tid	token	lemma	pos
cana-3215	1	1	communications	communication	NOUN
cana-3215	1	2	on	on	ADP
cana-3215	1	3	applied	apply	VERB
cana-3215	1	4	nonlinear	nonlinear	ADJ
cana-3215	1	5	analysis	analysis	NOUN
cana-3215	1	6	issn	issn	NOUN
cana-3215	1	7	:	:	PUNCT
cana-3215	1	8	1074	1074	NUM
cana-3215	1	9	-	-	PUNCT
cana-3215	1	10	133x	133x	NUM
cana-3215	1	11	vol	vol	NOUN
cana-3215	1	12	32	32	NUM
cana-3215	1	13	no	no	NOUN
cana-3215	1	14	.	.	PUNCT
cana-3215	2	1	6s	6s	NUM
cana-3215	2	2	(	(	PUNCT
cana-3215	2	3	2025	2025	NUM
cana-3215	2	4	)	)	PUNCT
cana-3215	2	5	16	16	NUM
cana-3215	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3215	2	7	visualizing	visualize	VERB
cana-3215	2	8	and	and	CCONJ
cana-3215	2	9	proving	prove	VERB
cana-3215	2	10	the	the	DET
cana-3215	2	11	collatz	collatz	NOUN
cana-3215	2	12	conjecture	conjecture	VERB
cana-3215	2	13	:	:	PUNCT
cana-3215	2	14	ananta	ananta	NOUN
cana-3215	2	15	-	-	PUNCT
cana-3215	2	16	graph	graph	NOUN
cana-3215	2	17	approach	approach	NOUN
cana-3215	2	18	vidyashree	vidyashree	NOUN
cana-3215	2	19	h	h	PROPN
cana-3215	2	20	r(a)(b	r(a)(b	NUM
cana-3215	2	21	)	)	PUNCT
cana-3215	2	22	,	,	PUNCT
cana-3215	2	23	lakshminarayana	lakshminarayana	PROPN
cana-3215	2	24	s(a	s(a	PROPN
cana-3215	2	25	)	)	PUNCT
cana-3215	2	26	,	,	PUNCT
cana-3215	2	27	ajith	ajith	PROPN
cana-3215	2	28	s(b	s(b	PROPN
cana-3215	2	29	)	)	PUNCT
cana-3215	2	30	(	(	PUNCT
cana-3215	2	31	a)reva	a)reva	X
cana-3215	2	32	university	university	PROPN
cana-3215	2	33	,	,	PUNCT
cana-3215	2	34	bengaluru	bengaluru	PROPN
cana-3215	2	35	.	.	PUNCT
cana-3215	3	1	(	(	PUNCT
cana-3215	3	2	b)nagarjuna	b)nagarjuna	PROPN
cana-3215	3	3	college	college	PROPN
cana-3215	3	4	of	of	ADP
cana-3215	3	5	management	management	NOUN
cana-3215	3	6	studies	study	NOUN
cana-3215	3	7	,	,	PUNCT
cana-3215	3	8	bengaluru	bengaluru	PROPN
cana-3215	3	9	.	.	PUNCT
cana-3215	4	1	email	email	NOUN
cana-3215	5	1	i	i	PROPN
cana-3215	5	2	d	d	PROPN
cana-3215	5	3	:	:	PUNCT
cana-3215	5	4	vidyashree848@gmail.com	vidyashree848@gmail.com	NUM
cana-3215	5	5	,	,	PUNCT
cana-3215	5	6	narayan_sl@reva.edu.in	narayan_sl@reva.edu.in	PROPN
cana-3215	5	7	,	,	PUNCT
cana-3215	5	8	ajith.sdl@gmail.com	ajith.sdl@gmail.com	PROPN
cana-3215	5	9	article	article	NOUN
cana-3215	5	10	history	history	NOUN
cana-3215	5	11	:	:	PUNCT
cana-3215	5	12	received	receive	VERB
cana-3215	5	13	:	:	PUNCT
cana-3215	5	14	13	13	NUM
cana-3215	5	15	-	-	SYM
cana-3215	5	16	10	10	NUM
cana-3215	5	17	-	-	PUNCT
cana-3215	5	18	2024	2024	NUM
cana-3215	5	19	revised	revise	VERB
cana-3215	5	20	:	:	PUNCT
cana-3215	5	21	28	28	NUM
cana-3215	5	22	-	-	SYM
cana-3215	5	23	11	11	NUM
cana-3215	5	24	-	-	PUNCT
cana-3215	5	25	2024	2024	NUM
cana-3215	5	26	accepted	accept	VERB
cana-3215	5	27	:	:	PUNCT
cana-3215	5	28	09	09	NUM
cana-3215	5	29	-	-	SYM
cana-3215	5	30	12	12	NUM
cana-3215	5	31	-	-	PUNCT
cana-3215	5	32	2024	2024	NUM
cana-3215	5	33	abstract	abstract	NOUN
cana-3215	5	34	:	:	PUNCT
cana-3215	5	35	the	the	DET
cana-3215	5	36	collatz	collatz	NOUN
cana-3215	5	37	conjecture	conjecture	VERB
cana-3215	5	38	,	,	PUNCT
cana-3215	5	39	proposed	propose	VERB
cana-3215	5	40	by	by	ADP
cana-3215	5	41	lothar	lothar	PROPN
cana-3215	5	42	collatz	collatz	PROPN
cana-3215	5	43	in	in	ADP
cana-3215	5	44	1937	1937	NUM
cana-3215	5	45	,	,	PUNCT
cana-3215	5	46	is	be	AUX
cana-3215	5	47	an	an	DET
cana-3215	5	48	unsolved	unsolved	ADJ
cana-3215	5	49	mathematical	mathematical	ADJ
cana-3215	5	50	problem	problem	NOUN
cana-3215	5	51	often	often	ADV
cana-3215	5	52	called	call	VERB
cana-3215	5	53	the	the	DET
cana-3215	5	54	“	"	PUNCT
cana-3215	5	55	3x+1	3x+1	ADJ
cana-3215	5	56	problem	problem	NOUN
cana-3215	5	57	”	"	PUNCT
cana-3215	5	58	or	or	CCONJ
cana-3215	5	59	the	the	DET
cana-3215	5	60	“	"	PUNCT
cana-3215	5	61	hailstone	hailstone	NOUN
cana-3215	5	62	sequence	sequence	NOUN
cana-3215	5	63	”	"	PUNCT
cana-3215	5	64	.	.	PUNCT
cana-3215	6	1	it	it	PRON
cana-3215	6	2	suggests	suggest	VERB
cana-3215	6	3	that	that	SCONJ
cana-3215	6	4	starting	start	VERB
cana-3215	6	5	with	with	ADP
cana-3215	6	6	any	any	DET
cana-3215	6	7	positive	positive	ADJ
cana-3215	6	8	integer	integer	NOUN
cana-3215	6	9	and	and	CCONJ
cana-3215	6	10	applying	apply	VERB
cana-3215	6	11	a	a	DET
cana-3215	6	12	specific	specific	ADJ
cana-3215	6	13	process	process	NOUN
cana-3215	6	14	:	:	PUNCT
cana-3215	6	15	dividing	divide	VERB
cana-3215	6	16	an	an	DET
cana-3215	6	17	even	even	ADJ
cana-3215	6	18	number	number	NOUN
cana-3215	6	19	by	by	ADP
cana-3215	6	20	2	2	NUM
cana-3215	6	21	or	or	CCONJ
cana-3215	6	22	multiplying	multiply	VERB
cana-3215	6	23	an	an	DET
cana-3215	6	24	odd	odd	ADJ
cana-3215	6	25	number	number	NOUN
cana-3215	6	26	by	by	ADP
cana-3215	6	27	3	3	NUM
cana-3215	6	28	and	and	CCONJ
cana-3215	6	29	adding	add	VERB
cana-3215	6	30	1	1	NUM
cana-3215	6	31	will	will	AUX
cana-3215	6	32	eventually	eventually	ADV
cana-3215	6	33	result	result	VERB
cana-3215	6	34	in	in	ADP
cana-3215	6	35	the	the	DET
cana-3215	6	36	sequence	sequence	NOUN
cana-3215	6	37	reaching	reach	VERB
cana-3215	6	38	the	the	DET
cana-3215	6	39	cycle	cycle	NOUN
cana-3215	6	40	4	4	NUM
cana-3215	6	41	,	,	PUNCT
cana-3215	6	42	2	2	NUM
cana-3215	6	43	,	,	PUNCT
cana-3215	6	44	1	1	NUM
cana-3215	6	45	regardless	regardless	ADV
cana-3215	6	46	of	of	ADP
cana-3215	6	47	the	the	DET
cana-3215	6	48	starting	starting	NOUN
cana-3215	6	49	value	value	NOUN
cana-3215	6	50	.	.	PUNCT
cana-3215	7	1	despite	despite	SCONJ
cana-3215	7	2	its	its	PRON
cana-3215	7	3	simplicity	simplicity	NOUN
cana-3215	7	4	,	,	PUNCT
cana-3215	7	5	no	no	DET
cana-3215	7	6	one	one	NOUN
cana-3215	7	7	has	have	AUX
cana-3215	7	8	been	be	AUX
cana-3215	7	9	able	able	ADJ
cana-3215	7	10	to	to	PART
cana-3215	7	11	prove	prove	VERB
cana-3215	7	12	or	or	CCONJ
cana-3215	7	13	disprove	disprove	VERB
cana-3215	7	14	this	this	DET
cana-3215	7	15	conjecture	conjecture	NOUN
cana-3215	7	16	for	for	ADP
cana-3215	7	17	all	all	DET
cana-3215	7	18	positive	positive	ADJ
cana-3215	7	19	numbers	number	NOUN
cana-3215	7	20	.	.	PUNCT
cana-3215	8	1	the	the	DET
cana-3215	8	2	behaviour	behaviour	NOUN
cana-3215	8	3	of	of	ADP
cana-3215	8	4	the	the	DET
cana-3215	8	5	collatz	collatz	NOUN
cana-3215	8	6	conjecture	conjecture	NOUN
cana-3215	8	7	can	can	AUX
cana-3215	8	8	also	also	ADV
cana-3215	8	9	be	be	AUX
cana-3215	8	10	illustrated	illustrate	VERB
cana-3215	8	11	through	through	ADP
cana-3215	8	12	a	a	DET
cana-3215	8	13	graphical	graphical	ADJ
cana-3215	8	14	representation	representation	NOUN
cana-3215	8	15	,	,	PUNCT
cana-3215	8	16	showing	show	VERB
cana-3215	8	17	how	how	SCONJ
cana-3215	8	18	the	the	DET
cana-3215	8	19	sequence	sequence	NOUN
cana-3215	8	20	for	for	ADP
cana-3215	8	21	different	different	ADJ
cana-3215	8	22	starting	starting	NOUN
cana-3215	8	23	numbers	number	NOUN
cana-3215	8	24	evolves	evolve	VERB
cana-3215	8	25	before	before	ADP
cana-3215	8	26	reaching	reach	VERB
cana-3215	8	27	the	the	DET
cana-3215	8	28	repeating	repeat	VERB
cana-3215	8	29	cycle	cycle	NOUN
cana-3215	8	30	of	of	ADP
cana-3215	8	31	4	4	NUM
cana-3215	8	32	,	,	PUNCT
cana-3215	8	33	2	2	NUM
cana-3215	8	34	,	,	PUNCT
cana-3215	8	35	1	1	NUM
cana-3215	8	36	.	.	PUNCT
cana-3215	9	1	in	in	ADP
cana-3215	9	2	this	this	DET
cana-3215	9	3	paper	paper	NOUN
cana-3215	9	4	,	,	PUNCT
cana-3215	9	5	we	we	PRON
cana-3215	9	6	highlight	highlight	VERB
cana-3215	9	7	the	the	DET
cana-3215	9	8	various	various	ADJ
cana-3215	9	9	graphical	graphical	ADJ
cana-3215	9	10	representations	representation	NOUN
cana-3215	9	11	of	of	ADP
cana-3215	9	12	the	the	DET
cana-3215	9	13	collatz	collatz	NOUN
cana-3215	9	14	sequence	sequence	NOUN
cana-3215	9	15	and	and	CCONJ
cana-3215	9	16	finally	finally	ADV
cana-3215	9	17	provide	provide	VERB
cana-3215	9	18	the	the	DET
cana-3215	9	19	proof	proof	NOUN
cana-3215	9	20	of	of	ADP
cana-3215	9	21	collatz	collatz	NOUN
cana-3215	9	22	conjecture	conjecture	NOUN
cana-3215	9	23	by	by	ADP
cana-3215	9	24	plotting	plot	VERB
cana-3215	9	25	the	the	DET
cana-3215	9	26	ananta	ananta	NOUN
cana-3215	9	27	-	-	PUNCT
cana-3215	9	28	graphs	graph	NOUN
cana-3215	9	29	.	.	PUNCT
cana-3215	10	1	keywords	keyword	NOUN
cana-3215	10	2	:	:	PUNCT
cana-3215	10	3	collatz	collatz	NOUN
cana-3215	10	4	sequence	sequence	NOUN
cana-3215	10	5	,	,	PUNCT
cana-3215	10	6	flower	flower	NOUN
cana-3215	10	7	pattern	pattern	NOUN
cana-3215	10	8	,	,	PUNCT
cana-3215	10	9	3x+1	3x+1	ADJ
cana-3215	10	10	sequence	sequence	NOUN
cana-3215	10	11	,	,	PUNCT
cana-3215	10	12	ananta	ananta	NOUN
cana-3215	10	13	-	-	PUNCT
cana-3215	10	14	graphs	graph	NOUN
cana-3215	10	15	.	.	PUNCT
cana-3215	11	1	introduction	introduction	NOUN
cana-3215	11	2	:	:	PUNCT
cana-3215	11	3	definition	definition	NOUN
cana-3215	11	4	1	1	NUM
cana-3215	11	5	:	:	PUNCT
cana-3215	11	6	the	the	DET
cana-3215	11	7	collatz	collatz	NOUN
cana-3215	11	8	sequence	sequence	NOUN
cana-3215	11	9	is	be	AUX
cana-3215	11	10	the	the	DET
cana-3215	11	11	sequence	sequence	NOUN
cana-3215	11	12	of	of	ADP
cana-3215	11	13	numbers	number	NOUN
cana-3215	11	14	generated	generate	VERB
cana-3215	11	15	by	by	ADP
cana-3215	11	16	the	the	DET
cana-3215	11	17	iterative	iterative	NOUN
cana-3215	11	18	process	process	NOUN
cana-3215	11	19	defined	define	VERB
cana-3215	11	20	by	by	ADP
cana-3215	11	21	the	the	DET
cana-3215	11	22	collatz	collatz	NOUN
cana-3215	11	23	conjecture	conjecture	NOUN
cana-3215	11	24	.	.	PUNCT
cana-3215	12	1	starting	start	VERB
cana-3215	12	2	from	from	ADP
cana-3215	12	3	any	any	DET
cana-3215	12	4	positive	positive	ADJ
cana-3215	12	5	integer	integer	NOUN
cana-3215	12	6	,	,	PUNCT
cana-3215	12	7	the	the	DET
cana-3215	12	8	sequence	sequence	NOUN
cana-3215	12	9	is	be	AUX
cana-3215	12	10	formed	form	VERB
cana-3215	12	11	by	by	ADP
cana-3215	12	12	applying	apply	VERB
cana-3215	12	13	the	the	DET
cana-3215	12	14	following	follow	VERB
cana-3215	12	15	rules	rule	NOUN
cana-3215	12	16	:	:	PUNCT
cana-3215	12	17	•	•	ADP
cana-3215	12	18	if	if	SCONJ
cana-3215	12	19	the	the	DET
cana-3215	12	20	number	number	NOUN
cana-3215	12	21	is	be	AUX
cana-3215	12	22	even	even	ADV
cana-3215	12	23	,	,	PUNCT
cana-3215	12	24	divide	divide	VERB
cana-3215	12	25	it	it	PRON
cana-3215	12	26	by	by	ADP
cana-3215	12	27	2	2	NUM
cana-3215	12	28	.	.	NOUN
cana-3215	12	29	•	•	NOUN
cana-3215	12	30	if	if	SCONJ
cana-3215	12	31	the	the	DET
cana-3215	12	32	number	number	NOUN
cana-3215	12	33	is	be	AUX
cana-3215	12	34	odd	odd	ADJ
cana-3215	12	35	,	,	PUNCT
cana-3215	12	36	multiply	multiply	VERB
cana-3215	12	37	it	it	PRON
cana-3215	12	38	by	by	ADP
cana-3215	12	39	3	3	NUM
cana-3215	12	40	and	and	CCONJ
cana-3215	12	41	add	add	VERB
cana-3215	12	42	1	1	NUM
cana-3215	12	43	.	.	NOUN
cana-3215	12	44	•	•	NOUN
cana-3215	12	45	repeat	repeat	VERB
cana-3215	12	46	this	this	DET
cana-3215	12	47	process	process	NOUN
cana-3215	12	48	with	with	ADP
cana-3215	12	49	the	the	DET
cana-3215	12	50	resulting	result	VERB
cana-3215	12	51	number	number	NOUN
cana-3215	12	52	until	until	SCONJ
cana-3215	12	53	you	you	PRON
cana-3215	12	54	reach	reach	VERB
cana-3215	12	55	1	1	NUM
cana-3215	12	56	,	,	PUNCT
cana-3215	12	57	at	at	ADP
cana-3215	12	58	which	which	DET
cana-3215	12	59	point	point	NOUN
cana-3215	12	60	the	the	DET
cana-3215	12	61	sequence	sequence	NOUN
cana-3215	12	62	will	will	AUX
cana-3215	12	63	enter	enter	VERB
cana-3215	12	64	the	the	DET
cana-3215	12	65	repeating	repeat	VERB
cana-3215	12	66	cycle	cycle	NOUN
cana-3215	12	67	of	of	ADP
cana-3215	12	68	4	4	NUM
cana-3215	12	69	,	,	PUNCT
cana-3215	12	70	2	2	NUM
cana-3215	12	71	,	,	PUNCT
cana-3215	12	72	1	1	NUM
cana-3215	12	73	.	.	PUNCT
cana-3215	12	74	communications	communication	NOUN
cana-3215	12	75	on	on	ADP
cana-3215	12	76	applied	apply	VERB
cana-3215	12	77	nonlinear	nonlinear	ADJ
cana-3215	12	78	analysis	analysis	NOUN
cana-3215	12	79	issn	issn	NOUN
cana-3215	12	80	:	:	PUNCT
cana-3215	12	81	1074	1074	NUM
cana-3215	12	82	-	-	PUNCT
cana-3215	12	83	133x	133x	NUM
cana-3215	12	84	vol	vol	NOUN
cana-3215	12	85	32	32	NUM
cana-3215	12	86	no	no	NOUN
cana-3215	12	87	.	.	PUNCT
cana-3215	13	1	6s	6s	NUM
cana-3215	13	2	(	(	PUNCT
cana-3215	13	3	2025	2025	NUM
cana-3215	13	4	)	)	PUNCT
cana-3215	13	5	17	17	NUM
cana-3215	13	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3215	13	7	example	example	NOUN
cana-3215	13	8	:	:	PUNCT
cana-3215	13	9	starting	start	VERB
cana-3215	13	10	with	with	ADP
cana-3215	13	11	n=13	n=13	PROPN
cana-3215	13	12	(	(	PUNCT
cana-3215	13	13	odd	odd	ADJ
cana-3215	13	14	)	)	PUNCT
cana-3215	13	15	13	13	NUM
cana-3215	13	16	*	*	SYM
cana-3215	13	17	3	3	NUM
cana-3215	13	18	+	+	SYM
cana-3215	13	19	1	1	NUM
cana-3215	13	20	=	=	SYM
cana-3215	13	21	40	40	NUM
cana-3215	13	22	(	(	PUNCT
cana-3215	13	23	even	even	ADV
cana-3215	13	24	)	)	PUNCT
cana-3215	13	25	40/2	40/2	PROPN
cana-3215	14	1	=	=	SYM
cana-3215	14	2	20	20	NUM
cana-3215	14	3	(	(	PUNCT
cana-3215	14	4	even	even	ADV
cana-3215	14	5	)	)	PUNCT
cana-3215	14	6	20/2	20/2	PROPN
cana-3215	15	1	=	=	SYM
cana-3215	15	2	10	10	NUM
cana-3215	15	3	(	(	PUNCT
cana-3215	15	4	even	even	ADV
cana-3215	15	5	)	)	PUNCT
cana-3215	15	6	10/2	10/2	X
cana-3215	15	7	=	=	SYM
cana-3215	15	8	5	5	NUM
cana-3215	15	9	(	(	PUNCT
cana-3215	15	10	odd	odd	ADJ
cana-3215	15	11	)	)	PUNCT
cana-3215	15	12	5	5	NUM
cana-3215	15	13	*	*	SYM
cana-3215	15	14	3	3	NUM
cana-3215	15	15	+	+	SYM
cana-3215	15	16	1	1	NUM
cana-3215	15	17	=	=	SYM
cana-3215	15	18	16	16	NUM
cana-3215	15	19	(	(	PUNCT
cana-3215	15	20	even	even	ADV
cana-3215	15	21	)	)	PUNCT
cana-3215	15	22	16/2	16/2	PROPN
cana-3215	15	23	=	=	SYM
cana-3215	15	24	8	8	NUM
cana-3215	15	25	(	(	PUNCT
cana-3215	15	26	even	even	ADV
cana-3215	15	27	)	)	PUNCT
cana-3215	15	28	8/2	8/2	NUM
cana-3215	15	29	=	=	SYM
cana-3215	15	30	4	4	NUM
cana-3215	15	31	(	(	PUNCT
cana-3215	15	32	even	even	ADV
cana-3215	15	33	)	)	PUNCT
cana-3215	15	34	4/2	4/2	NUM
cana-3215	15	35	=	=	SYM
cana-3215	15	36	2	2	NUM
cana-3215	15	37	(	(	PUNCT
cana-3215	15	38	even	even	ADV
cana-3215	15	39	)	)	PUNCT
cana-3215	15	40	2/2	2/2	NUM
cana-3215	15	41	=	=	SYM
cana-3215	15	42	1	1	NUM
cana-3215	15	43	(	(	PUNCT
cana-3215	15	44	sequence	sequence	NOUN
cana-3215	15	45	ends	end	VERB
cana-3215	15	46	)	)	PUNCT
cana-3215	15	47	the	the	DET
cana-3215	15	48	sequence	sequence	NOUN
cana-3215	15	49	for	for	ADP
cana-3215	15	50	n=7	n=7	PROPN
cana-3215	15	51	is	be	AUX
cana-3215	15	52	:	:	PUNCT
cana-3215	15	53	7	7	NUM
cana-3215	15	54	,	,	PUNCT
cana-3215	15	55	22	22	NUM
cana-3215	15	56	,	,	PUNCT
cana-3215	15	57	11	11	NUM
cana-3215	15	58	,	,	PUNCT
cana-3215	15	59	34	34	NUM
cana-3215	15	60	,	,	PUNCT
cana-3215	15	61	17	17	NUM
cana-3215	15	62	,	,	PUNCT
cana-3215	15	63	52	52	NUM
cana-3215	15	64	,	,	PUNCT
cana-3215	15	65	26	26	NUM
cana-3215	15	66	,	,	PUNCT
cana-3215	15	67	13	13	NUM
cana-3215	15	68	,	,	PUNCT
cana-3215	15	69	40	40	NUM
cana-3215	15	70	,	,	PUNCT
cana-3215	15	71	20	20	NUM
cana-3215	15	72	,	,	PUNCT
cana-3215	15	73	10	10	NUM
cana-3215	15	74	,	,	PUNCT
cana-3215	15	75	5	5	NUM
cana-3215	15	76	,	,	PUNCT
cana-3215	15	77	16	16	NUM
cana-3215	15	78	,	,	PUNCT
cana-3215	15	79	8	8	NUM
cana-3215	15	80	,	,	PUNCT
cana-3215	15	81	4	4	NUM
cana-3215	15	82	,	,	PUNCT
cana-3215	15	83	2	2	NUM
cana-3215	15	84	,	,	PUNCT
cana-3215	15	85	1	1	NUM
cana-3215	15	86	.	.	X
cana-3215	15	87	definition	definition	NOUN
cana-3215	15	88	2	2	NUM
cana-3215	15	89	:	:	PUNCT
cana-3215	15	90	ananta	ananta	NOUN
cana-3215	15	91	-	-	PUNCT
cana-3215	15	92	graphs	graph	NOUN
cana-3215	15	93	are	be	AUX
cana-3215	15	94	a	a	DET
cana-3215	15	95	graphical	graphical	ADJ
cana-3215	15	96	representation	representation	NOUN
cana-3215	15	97	based	base	VERB
cana-3215	15	98	on	on	ADP
cana-3215	15	99	the	the	DET
cana-3215	15	100	collatz	collatz	NOUN
cana-3215	15	101	conjecture	conjecture	NOUN
cana-3215	15	102	(	(	PUNCT
cana-3215	15	103	also	also	ADV
cana-3215	15	104	known	know	VERB
cana-3215	15	105	as	as	ADP
cana-3215	15	106	the	the	DET
cana-3215	15	107	3x+1	3x+1	PROPN
cana-3215	15	108	problem	problem	NOUN
cana-3215	15	109	)	)	PUNCT
cana-3215	15	110	.	.	PUNCT
cana-3215	16	1	the	the	DET
cana-3215	16	2	graph	graph	NOUN
cana-3215	16	3	visually	visually	ADV
cana-3215	16	4	illustrates	illustrate	VERB
cana-3215	16	5	the	the	DET
cana-3215	16	6	sequence	sequence	NOUN
cana-3215	16	7	of	of	ADP
cana-3215	16	8	numbers	number	NOUN
cana-3215	16	9	that	that	PRON
cana-3215	16	10	follow	follow	VERB
cana-3215	16	11	the	the	DET
cana-3215	16	12	conjecture	conjecture	NOUN
cana-3215	16	13	’s	’s	PART
cana-3215	16	14	rules	rule	NOUN
cana-3215	16	15	and	and	CCONJ
cana-3215	16	16	ultimately	ultimately	ADV
cana-3215	16	17	fall	fall	VERB
cana-3215	16	18	into	into	ADP
cana-3215	16	19	a	a	DET
cana-3215	16	20	repeating	repeat	VERB
cana-3215	16	21	cycle	cycle	NOUN
cana-3215	16	22	.	.	PUNCT
cana-3215	17	1	the	the	DET
cana-3215	17	2	term	term	NOUN
cana-3215	17	3	“	"	PUNCT
cana-3215	17	4	ananta	ananta	NOUN
cana-3215	17	5	”	"	PUNCT
cana-3215	17	6	(	(	PUNCT
cana-3215	17	7	sanskrit	sanskrit	NOUN
cana-3215	17	8	for	for	ADP
cana-3215	17	9	“	"	PUNCT
cana-3215	17	10	infinite	infinite	VERB
cana-3215	17	11	”	"	PUNCT
cana-3215	17	12	or	or	CCONJ
cana-3215	17	13	“	"	PUNCT
cana-3215	17	14	endless	endless	ADJ
cana-3215	17	15	”	"	PUNCT
cana-3215	17	16	)	)	PUNCT
cana-3215	17	17	reflects	reflect	VERB
cana-3215	17	18	the	the	DET
cana-3215	17	19	unbounded	unbounded	ADJ
cana-3215	17	20	nature	nature	NOUN
cana-3215	17	21	of	of	ADP
cana-3215	17	22	the	the	DET
cana-3215	17	23	positive	positive	ADJ
cana-3215	17	24	integers	integer	NOUN
cana-3215	17	25	involved	involve	VERB
cana-3215	17	26	in	in	ADP
cana-3215	17	27	the	the	DET
cana-3215	17	28	graph	graph	NOUN
cana-3215	17	29	.	.	PUNCT
cana-3215	18	1	structure	structure	NOUN
cana-3215	18	2	of	of	ADP
cana-3215	18	3	the	the	DET
cana-3215	18	4	ananta	ananta	NOUN
cana-3215	18	5	-	-	PUNCT
cana-3215	18	6	graph	graph	NOUN
cana-3215	18	7	:	:	PUNCT
cana-3215	18	8	•	•	NUM
cana-3215	18	9	triangular	triangular	NOUN
cana-3215	18	10	head	head	NOUN
cana-3215	18	11	:	:	PUNCT
cana-3215	18	12	the	the	DET
cana-3215	18	13	key	key	ADJ
cana-3215	18	14	feature	feature	NOUN
cana-3215	18	15	of	of	ADP
cana-3215	18	16	the	the	DET
cana-3215	18	17	ananta	ananta	NOUN
cana-3215	18	18	-	-	PUNCT
cana-3215	18	19	graph	graph	NOUN
cana-3215	18	20	is	be	AUX
cana-3215	18	21	the	the	DET
cana-3215	18	22	triangular	triangular	NOUN
cana-3215	18	23	cycle	cycle	NOUN
cana-3215	18	24	formed	form	VERB
cana-3215	18	25	by	by	ADP
cana-3215	18	26	the	the	DET
cana-3215	18	27	vertices	vertex	NOUN
cana-3215	18	28	4	4	NUM
cana-3215	18	29	,	,	PUNCT
cana-3215	18	30	2	2	NUM
cana-3215	18	31	and	and	CCONJ
cana-3215	18	32	1	1	NUM
cana-3215	18	33	.	.	PUNCT
cana-3215	19	1	this	this	PRON
cana-3215	19	2	forms	form	VERB
cana-3215	19	3	a	a	DET
cana-3215	19	4	closed	closed	ADJ
cana-3215	19	5	loop	loop	NOUN
cana-3215	19	6	that	that	PRON
cana-3215	19	7	is	be	AUX
cana-3215	19	8	the	the	DET
cana-3215	19	9	final	final	ADJ
cana-3215	19	10	destination	destination	NOUN
cana-3215	19	11	of	of	ADP
cana-3215	19	12	all	all	DET
cana-3215	19	13	paths	path	NOUN
cana-3215	19	14	in	in	ADP
cana-3215	19	15	the	the	DET
cana-3215	19	16	graph	graph	NOUN
cana-3215	19	17	.	.	PUNCT
cana-3215	20	1	•	•	NUM
cana-3215	20	2	long	long	ADJ
cana-3215	20	3	tail	tail	NOUN
cana-3215	20	4	:	:	PUNCT
cana-3215	20	5	every	every	DET
cana-3215	20	6	other	other	ADJ
cana-3215	20	7	positive	positive	ADJ
cana-3215	20	8	integer	integer	NOUN
cana-3215	20	9	that	that	PRON
cana-3215	20	10	follows	follow	VERB
cana-3215	20	11	the	the	DET
cana-3215	20	12	collatz	collatz	NOUN
cana-3215	20	13	sequence	sequence	NOUN
cana-3215	20	14	eventually	eventually	ADV
cana-3215	20	15	converges	converge	VERB
cana-3215	20	16	toward	toward	ADP
cana-3215	20	17	this	this	DET
cana-3215	20	18	triangular	triangular	NOUN
cana-3215	20	19	cycle	cycle	NOUN
cana-3215	20	20	.	.	PUNCT
cana-3215	21	1	this	this	PRON
cana-3215	21	2	forms	form	VERB
cana-3215	21	3	the	the	DET
cana-3215	21	4	“	"	PUNCT
cana-3215	21	5	tail	tail	NOUN
cana-3215	21	6	”	"	PUNCT
cana-3215	21	7	of	of	ADP
cana-3215	21	8	the	the	DET
cana-3215	21	9	graph	graph	NOUN
cana-3215	21	10	.	.	PUNCT
cana-3215	22	1	example	example	NOUN
cana-3215	22	2	:	:	PUNCT
cana-3215	22	3	for	for	ADP
cana-3215	22	4	n=13	n=13	PROPN
cana-3215	22	5	previous	previous	ADJ
cana-3215	22	6	results	result	NOUN
cana-3215	22	7	:	:	PUNCT
cana-3215	22	8	the	the	DET
cana-3215	22	9	collatz	collatz	NOUN
cana-3215	22	10	graphs	graph	NOUN
cana-3215	22	11	are	be	AUX
cana-3215	22	12	explored	explore	VERB
cana-3215	22	13	by	by	ADP
cana-3215	22	14	analyzing	analyze	VERB
cana-3215	22	15	the	the	DET
cana-3215	22	16	3n+1	3n+1	PROPN
cana-3215	22	17	function	function	NOUN
cana-3215	22	18	on	on	ADP
cana-3215	22	19	congruence	congruence	PROPN
cana-3215	22	20	classes	class	NOUN
cana-3215	22	21	,	,	PUNCT
cana-3215	22	22	focusing	focus	VERB
cana-3215	22	23	on	on	ADP
cana-3215	22	24	moduli	modulus	NOUN
cana-3215	22	25	that	that	PRON
cana-3215	22	26	are	be	AUX
cana-3215	22	27	powers	power	NOUN
cana-3215	22	28	of	of	ADP
cana-3215	22	29	2	2	NUM
cana-3215	22	30	.	.	PUNCT
cana-3215	23	1	these	these	DET
cana-3215	23	2	graphs	graph	NOUN
cana-3215	23	3	are	be	AUX
cana-3215	23	4	isomorphic	isomorphic	ADJ
cana-3215	23	5	to	to	ADP
cana-3215	23	6	binary	binary	PROPN
cana-3215	23	7	de	de	PROPN
cana-3215	23	8	bruijn	bruijn	NOUN
cana-3215	23	9	graphs	graph	NOUN
cana-3215	23	10	,	,	PUNCT
cana-3215	23	11	which	which	PRON
cana-3215	23	12	are	be	AUX
cana-3215	23	13	wellstructured	wellstructure	VERB
cana-3215	23	14	and	and	CCONJ
cana-3215	23	15	display	display	VERB
cana-3215	23	16	intriguing	intriguing	ADJ
cana-3215	23	17	properties	property	NOUN
cana-3215	23	18	.	.	PUNCT
cana-3215	24	1	the	the	DET
cana-3215	24	2	research	research	NOUN
cana-3215	24	3	further	far	ADV
cana-3215	24	4	extends	extend	VERB
cana-3215	24	5	to	to	ADP
cana-3215	24	6	2	2	NUM
cana-3215	24	7	-	-	PUNCT
cana-3215	24	8	adic	adic	ADJ
cana-3215	24	9	integers	integer	NOUN
cana-3215	24	10	,	,	PUNCT
cana-3215	24	11	revealing	reveal	VERB
cana-3215	24	12	that	that	SCONJ
cana-3215	24	13	the	the	DET
cana-3215	24	14	isomorphism	isomorphism	NOUN
cana-3215	24	15	of	of	ADP
cana-3215	24	16	these	these	DET
cana-3215	24	17	infinite	infinite	ADJ
cana-3215	24	18	graphs	graph	NOUN
cana-3215	24	19	aligns	align	VERB
cana-3215	24	20	with	with	ADP
cana-3215	24	21	the	the	DET
cana-3215	24	22	conjugacy	conjugacy	PROPN
cana-3215	24	23	map	map	NOUN
cana-3215	24	24	previously	previously	ADV
cana-3215	24	25	examined	examine	VERB
cana-3215	24	26	by	by	ADP
cana-3215	24	27	bernstein	bernstein	PROPN
cana-3215	24	28	and	and	CCONJ
cana-3215	24	29	lagarias	lagaria	NOUN
cana-3215	25	1	[	[	X
cana-3215	25	2	1	1	NUM
cana-3215	25	3	]	]	PUNCT
cana-3215	25	4	.	.	PUNCT
cana-3215	26	1	to	to	PART
cana-3215	26	2	study	study	VERB
cana-3215	26	3	the	the	DET
cana-3215	26	4	collatz	collatz	NOUN
cana-3215	26	5	conjecture	conjecture	VERB
cana-3215	26	6	,	,	PUNCT
cana-3215	26	7	the	the	DET
cana-3215	26	8	paper	paper	NOUN
cana-3215	27	1	[	[	X
cana-3215	27	2	2	2	NUM
cana-3215	27	3	]	]	PUNCT
cana-3215	27	4	introduces	introduce	VERB
cana-3215	27	5	a	a	DET
cana-3215	27	6	clustering	cluster	VERB
cana-3215	27	7	approach	approach	NOUN
cana-3215	27	8	using	use	VERB
cana-3215	27	9	hierarchical	hierarchical	ADJ
cana-3215	27	10	clustering	clustering	NOUN
cana-3215	27	11	(	(	PUNCT
cana-3215	27	12	hc	hc	NOUN
cana-3215	27	13	)	)	PUNCT
cana-3215	27	14	and	and	CCONJ
cana-3215	27	15	multidimensional	multidimensional	ADJ
cana-3215	27	16	scaling	scaling	NOUN
cana-3215	27	17	(	(	PUNCT
cana-3215	27	18	mds	mds	NOUN
cana-3215	27	19	)	)	PUNCT
cana-3215	27	20	algorithms	algorithm	NOUN
cana-3215	27	21	.	.	PUNCT
cana-3215	28	1	hc	hc	PROPN
cana-3215	28	2	generates	generate	VERB
cana-3215	28	3	two	two	NUM
cana-3215	28	4	-	-	PUNCT
cana-3215	28	5	dimensional	dimensional	ADJ
cana-3215	28	6	graphical	graphical	ADJ
cana-3215	28	7	outputs	output	NOUN
cana-3215	28	8	like	like	ADP
cana-3215	28	9	dendrograms	dendrogram	NOUN
cana-3215	28	10	and	and	CCONJ
cana-3215	28	11	trees	tree	NOUN
cana-3215	28	12	,	,	PUNCT
cana-3215	28	13	while	while	SCONJ
cana-3215	28	14	mds	mds	NOUN
cana-3215	28	15	produces	produce	VERB
cana-3215	28	16	two	two	NUM
cana-3215	28	17	and	and	CCONJ
cana-3215	28	18	three	three	NUM
cana-3215	28	19	-	-	PUNCT
cana-3215	28	20	dimensional	dimensional	ADJ
cana-3215	28	21	charts	chart	NOUN
cana-3215	28	22	.	.	PUNCT
cana-3215	29	1	it	it	PRON
cana-3215	29	2	is	be	AUX
cana-3215	29	3	observed	observe	VERB
cana-3215	29	4	that	that	SCONJ
cana-3215	29	5	the	the	DET
cana-3215	29	6	three	three	NUM
cana-3215	29	7	-	-	PUNCT
cana-3215	29	8	dimensional	dimensional	ADJ
cana-3215	29	9	mds	mds	NOUN
cana-3215	29	10	map	map	NOUN
cana-3215	29	11	reveals	reveal	VERB
cana-3215	29	12	complex	complex	ADJ
cana-3215	29	13	patterns	pattern	NOUN
cana-3215	29	14	that	that	PRON
cana-3215	29	15	are	be	AUX
cana-3215	29	16	not	not	PART
cana-3215	29	17	easily	easily	ADV
cana-3215	29	18	seen	see	VERB
cana-3215	29	19	communications	communication	NOUN
cana-3215	29	20	on	on	ADP
cana-3215	29	21	applied	apply	VERB
cana-3215	29	22	nonlinear	nonlinear	ADJ
cana-3215	29	23	analysis	analysis	NOUN
cana-3215	29	24	issn	issn	NOUN
cana-3215	29	25	:	:	PUNCT
cana-3215	29	26	1074	1074	NUM
cana-3215	29	27	-	-	PUNCT
cana-3215	29	28	133x	133x	NUM
cana-3215	29	29	vol	vol	NOUN
cana-3215	29	30	32	32	NUM
cana-3215	29	31	no	no	NOUN
cana-3215	29	32	.	.	PUNCT
cana-3215	30	1	6s	6s	NUM
cana-3215	30	2	(	(	PUNCT
cana-3215	30	3	2025	2025	NUM
cana-3215	30	4	)	)	PUNCT
cana-3215	30	5	18	18	NUM
cana-3215	30	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3215	30	7	in	in	ADP
cana-3215	30	8	two	two	NUM
cana-3215	30	9	-	-	PUNCT
cana-3215	30	10	dimensional	dimensional	ADJ
cana-3215	30	11	visuals	visual	NOUN
cana-3215	30	12	.	.	PUNCT
cana-3215	31	1	the	the	DET
cana-3215	31	2	study	study	NOUN
cana-3215	31	3	tested	test	VERB
cana-3215	31	4	six	six	NUM
cana-3215	31	5	distance	distance	NOUN
cana-3215	31	6	metrics	metric	NOUN
cana-3215	31	7	combined	combine	VERB
cana-3215	31	8	with	with	ADP
cana-3215	31	9	hamming	ham	VERB
cana-3215	31	10	-	-	PUNCT
cana-3215	31	11	like	like	ADJ
cana-3215	31	12	classification	classification	NOUN
cana-3215	31	13	,	,	PUNCT
cana-3215	31	14	with	with	ADP
cana-3215	31	15	the	the	DET
cana-3215	31	16	arccosine	arccosine	NOUN
cana-3215	31	17	-	-	PUNCT
cana-3215	31	18	hamming	hamming	NOUN
cana-3215	31	19	,	,	PUNCT
cana-3215	31	20	canberra	canberra	NOUN
cana-3215	31	21	-	-	PUNCT
cana-3215	31	22	hamming	hamming	NOUN
cana-3215	31	23	and	and	CCONJ
cana-3215	31	24	clark	clark	NOUN
cana-3215	31	25	-	-	PUNCT
cana-3215	31	26	hamming	ham	VERB
cana-3215	31	27	distances	distance	NOUN
cana-3215	31	28	yielding	yield	VERB
cana-3215	31	29	the	the	DET
cana-3215	31	30	clearest	clear	ADJ
cana-3215	31	31	structures	structure	NOUN
cana-3215	31	32	in	in	ADP
cana-3215	31	33	the	the	DET
cana-3215	31	34	three	three	NUM
cana-3215	31	35	-	-	PUNCT
cana-3215	31	36	dimensional	dimensional	ADJ
cana-3215	31	37	mds	mds	NOUN
cana-3215	31	38	maps	map	NOUN
cana-3215	31	39	.	.	PUNCT
cana-3215	32	1	the	the	DET
cana-3215	32	2	collatz	collatz	PROPN
cana-3215	32	3	problem	problem	NOUN
cana-3215	32	4	was	be	AUX
cana-3215	32	5	examined	examine	VERB
cana-3215	32	6	through	through	ADP
cana-3215	32	7	the	the	DET
cana-3215	32	8	lens	lens	NOUN
cana-3215	32	9	of	of	ADP
cana-3215	32	10	graph	graph	NOUN
cana-3215	32	11	theory	theory	NOUN
cana-3215	32	12	and	and	CCONJ
cana-3215	32	13	the	the	DET
cana-3215	32	14	properties	property	NOUN
cana-3215	32	15	of	of	ADP
cana-3215	32	16	the	the	DET
cana-3215	32	17	digital	digital	ADJ
cana-3215	32	18	root	root	NOUN
cana-3215	32	19	of	of	ADP
cana-3215	32	20	natural	natural	ADJ
cana-3215	32	21	numbers	number	NOUN
cana-3215	32	22	.	.	PUNCT
cana-3215	33	1	a	a	DET
cana-3215	33	2	consistent	consistent	ADJ
cana-3215	33	3	pattern	pattern	NOUN
cana-3215	33	4	was	be	AUX
cana-3215	33	5	identified	identify	VERB
cana-3215	33	6	in	in	ADP
cana-3215	33	7	the	the	DET
cana-3215	33	8	iteration	iteration	NOUN
cana-3215	33	9	of	of	ADP
cana-3215	33	10	sequence	sequence	NOUN
cana-3215	33	11	numbers	number	NOUN
cana-3215	33	12	,	,	PUNCT
cana-3215	33	13	where	where	SCONJ
cana-3215	33	14	the	the	DET
cana-3215	33	15	digital	digital	ADJ
cana-3215	33	16	root	root	NOUN
cana-3215	33	17	follows	follow	VERB
cana-3215	33	18	a	a	DET
cana-3215	33	19	cyclic	cyclic	ADJ
cana-3215	33	20	order	order	NOUN
cana-3215	33	21	.	.	PUNCT
cana-3215	34	1	all	all	DET
cana-3215	34	2	numbers	number	NOUN
cana-3215	34	3	eventually	eventually	ADV
cana-3215	34	4	connect	connect	VERB
cana-3215	34	5	to	to	ADP
cana-3215	34	6	even	even	ADV
cana-3215	34	7	numbers	number	NOUN
cana-3215	34	8	with	with	ADP
cana-3215	34	9	a	a	DET
cana-3215	34	10	digital	digital	ADJ
cana-3215	34	11	root	root	NOUN
cana-3215	34	12	of	of	ADP
cana-3215	34	13	2	2	NUM
cana-3215	34	14	and	and	CCONJ
cana-3215	34	15	after	after	ADP
cana-3215	34	16	a	a	DET
cana-3215	34	17	series	series	NOUN
cana-3215	34	18	of	of	ADP
cana-3215	34	19	iterations	iteration	NOUN
cana-3215	34	20	and	and	CCONJ
cana-3215	34	21	cycles	cycle	NOUN
cana-3215	34	22	,	,	PUNCT
cana-3215	34	23	they	they	PRON
cana-3215	34	24	ultimately	ultimately	ADV
cana-3215	34	25	reach	reach	VERB
cana-3215	34	26	the	the	DET
cana-3215	34	27	number	number	NOUN
cana-3215	34	28	1	1	NUM
cana-3215	34	29	[	[	X
cana-3215	34	30	3	3	NUM
cana-3215	34	31	]	]	PUNCT
cana-3215	34	32	.	.	PUNCT
cana-3215	35	1	the	the	DET
cana-3215	35	2	collatz	collatz	PROPN
cana-3215	35	3	conjecture	conjecture	NOUN
cana-3215	35	4	was	be	AUX
cana-3215	35	5	analysed	analyse	VERB
cana-3215	35	6	by	by	ADP
cana-3215	35	7	constructing	construct	VERB
cana-3215	35	8	a	a	DET
cana-3215	35	9	directed	direct	VERB
cana-3215	35	10	graph	graph	NOUN
cana-3215	35	11	that	that	PRON
cana-3215	35	12	connects	connect	VERB
cana-3215	35	13	all	all	DET
cana-3215	35	14	natural	natural	ADJ
cana-3215	35	15	numbers	number	NOUN
cana-3215	35	16	.	.	PUNCT
cana-3215	36	1	it	it	PRON
cana-3215	36	2	confirms	confirm	VERB
cana-3215	36	3	that	that	SCONJ
cana-3215	36	4	the	the	DET
cana-3215	36	5	collatz	collatz	NOUN
cana-3215	36	6	sequences	sequence	NOUN
cana-3215	36	7	cover	cover	VERB
cana-3215	36	8	all	all	DET
cana-3215	36	9	positive	positive	ADJ
cana-3215	36	10	integers	integer	NOUN
cana-3215	36	11	and	and	CCONJ
cana-3215	36	12	importantly	importantly	ADV
cana-3215	36	13	,	,	PUNCT
cana-3215	36	14	do	do	AUX
cana-3215	36	15	not	not	PART
cana-3215	36	16	form	form	VERB
cana-3215	36	17	any	any	DET
cana-3215	36	18	nontrivial	nontrivial	ADJ
cana-3215	36	19	cycles	cycle	NOUN
cana-3215	36	20	,	,	PUNCT
cana-3215	36	21	reinforcing	reinforce	VERB
cana-3215	36	22	the	the	DET
cana-3215	36	23	hypothesis	hypothesis	NOUN
cana-3215	36	24	that	that	PRON
cana-3215	36	25	all	all	DET
cana-3215	36	26	sequences	sequence	NOUN
cana-3215	36	27	eventually	eventually	ADV
cana-3215	36	28	settle	settle	VERB
cana-3215	36	29	into	into	ADP
cana-3215	36	30	the	the	DET
cana-3215	36	31	trivial	trivial	ADJ
cana-3215	36	32	cycle	cycle	NOUN
cana-3215	36	33	of	of	ADP
cana-3215	36	34	1,2,1,2	1,2,1,2	NUM
cana-3215	36	35	and	and	CCONJ
cana-3215	36	36	so	so	ADV
cana-3215	36	37	on	on	ADV
cana-3215	36	38	.	.	PUNCT
cana-3215	37	1	this	this	PRON
cana-3215	37	2	illustrates	illustrate	VERB
cana-3215	37	3	the	the	DET
cana-3215	37	4	intricate	intricate	ADJ
cana-3215	37	5	relationship	relationship	NOUN
cana-3215	37	6	between	between	ADP
cana-3215	37	7	number	number	NOUN
cana-3215	37	8	theory	theory	NOUN
cana-3215	37	9	and	and	CCONJ
cana-3215	37	10	graph	graph	NOUN
cana-3215	37	11	theory	theory	NOUN
cana-3215	37	12	[	[	X
cana-3215	37	13	4	4	NUM
cana-3215	37	14	]	]	PUNCT
cana-3215	37	15	.	.	PUNCT
cana-3215	38	1	the	the	DET
cana-3215	38	2	collatz	collatz	NOUN
cana-3215	38	3	graph	graph	NOUN
cana-3215	38	4	was	be	AUX
cana-3215	38	5	constructed	construct	VERB
cana-3215	38	6	to	to	PART
cana-3215	38	7	address	address	VERB
cana-3215	38	8	the	the	DET
cana-3215	38	9	collatz	collatz	PROPN
cana-3215	38	10	problem	problem	NOUN
cana-3215	38	11	with	with	ADP
cana-3215	38	12	a	a	DET
cana-3215	38	13	regular	regular	ADJ
cana-3215	38	14	structure	structure	NOUN
cana-3215	38	15	.	.	PUNCT
cana-3215	39	1	using	use	VERB
cana-3215	39	2	a	a	DET
cana-3215	39	3	bottom	bottom	ADJ
cana-3215	39	4	-	-	PUNCT
cana-3215	39	5	up	up	ADP
cana-3215	39	6	approach	approach	NOUN
cana-3215	39	7	with	with	ADP
cana-3215	39	8	inverse	inverse	NOUN
cana-3215	39	9	relations	relation	NOUN
cana-3215	39	10	,	,	PUNCT
cana-3215	39	11	the	the	DET
cana-3215	39	12	graph	graph	NOUN
cana-3215	39	13	connects	connect	VERB
cana-3215	39	14	each	each	DET
cana-3215	39	15	number	number	NOUN
cana-3215	39	16	n	n	NOUN
cana-3215	39	17	to	to	ADP
cana-3215	39	18	its	its	PRON
cana-3215	39	19	predecessor	predecessor	NOUN
cana-3215	39	20	m	m	VERB
cana-3215	39	21	if	if	SCONJ
cana-3215	39	22	n	n	PRON
cana-3215	39	23	is	be	AUX
cana-3215	39	24	the	the	DET
cana-3215	39	25	collatz	collatz	NOUN
cana-3215	39	26	functional	functional	ADJ
cana-3215	39	27	value	value	NOUN
cana-3215	39	28	of	of	ADP
cana-3215	39	29	m.	m.	NOUN
cana-3215	39	30	the	the	DET
cana-3215	39	31	tree	tree	NOUN
cana-3215	39	32	-	-	PUNCT
cana-3215	39	33	like	like	ADJ
cana-3215	39	34	graph	graph	NOUN
cana-3215	39	35	demonstrates	demonstrate	VERB
cana-3215	39	36	that	that	SCONJ
cana-3215	39	37	for	for	ADP
cana-3215	39	38	any	any	DET
cana-3215	39	39	seed	seed	NOUN
cana-3215	39	40	n	n	CCONJ
cana-3215	39	41	,	,	PUNCT
cana-3215	39	42	the	the	DET
cana-3215	39	43	generated	generate	VERB
cana-3215	39	44	collatz	collatz	NOUN
cana-3215	39	45	sequences	sequence	NOUN
cana-3215	39	46	converge	converge	VERB
cana-3215	39	47	to	to	ADP
cana-3215	39	48	one	one	NUM
cana-3215	39	49	.	.	PUNCT
cana-3215	40	1	the	the	DET
cana-3215	40	2	simple	simple	ADJ
cana-3215	40	3	connection	connection	NOUN
cana-3215	40	4	rules	rule	NOUN
cana-3215	40	5	are	be	AUX
cana-3215	40	6	introduced	introduce	VERB
cana-3215	40	7	to	to	PART
cana-3215	40	8	build	build	VERB
cana-3215	40	9	the	the	DET
cana-3215	40	10	graph	graph	NOUN
cana-3215	40	11	,	,	PUNCT
cana-3215	40	12	ensuring	ensure	VERB
cana-3215	40	13	it	it	PRON
cana-3215	40	14	contains	contain	VERB
cana-3215	40	15	all	all	DET
cana-3215	40	16	the	the	DET
cana-3215	40	17	positive	positive	ADJ
cana-3215	40	18	numbers	number	NOUN
cana-3215	40	19	.	.	PUNCT
cana-3215	41	1	this	this	PRON
cana-3215	41	2	shows	show	VERB
cana-3215	41	3	that	that	SCONJ
cana-3215	41	4	the	the	DET
cana-3215	41	5	developed	develop	VERB
cana-3215	41	6	graph	graph	NOUN
cana-3215	41	7	generates	generate	VERB
cana-3215	41	8	collatz	collatz	NOUN
cana-3215	41	9	trajectories	trajectory	NOUN
cana-3215	41	10	for	for	ADP
cana-3215	41	11	all	all	DET
cana-3215	41	12	integers	integer	NOUN
cana-3215	41	13	[	[	X
cana-3215	41	14	5	5	NUM
cana-3215	41	15	]	]	PUNCT
cana-3215	41	16	.	.	PUNCT
cana-3215	42	1	despite	despite	SCONJ
cana-3215	42	2	extensive	extensive	ADJ
cana-3215	42	3	computational	computational	ADJ
cana-3215	42	4	verification	verification	NOUN
cana-3215	42	5	up	up	ADP
cana-3215	42	6	to	to	ADP
cana-3215	42	7	very	very	ADV
cana-3215	42	8	high	high	ADJ
cana-3215	42	9	numerical	numerical	ADJ
cana-3215	42	10	limits	limit	NOUN
cana-3215	42	11	,	,	PUNCT
cana-3215	42	12	no	no	DET
cana-3215	42	13	rigorous	rigorous	ADJ
cana-3215	42	14	mathematical	mathematical	ADJ
cana-3215	42	15	proof	proof	NOUN
cana-3215	42	16	has	have	AUX
cana-3215	42	17	been	be	AUX
cana-3215	42	18	found	find	VERB
cana-3215	42	19	to	to	PART
cana-3215	42	20	confirm	confirm	VERB
cana-3215	42	21	this	this	DET
cana-3215	42	22	conjecture	conjecture	NOUN
cana-3215	42	23	universally	universally	ADV
cana-3215	42	24	.	.	PUNCT
cana-3215	43	1	there	there	PRON
cana-3215	43	2	are	be	VERB
cana-3215	43	3	no	no	DET
cana-3215	43	4	infinite	infinite	ADJ
cana-3215	43	5	loops	loop	NOUN
cana-3215	43	6	existing	exist	VERB
cana-3215	43	7	in	in	ADP
cana-3215	43	8	the	the	DET
cana-3215	43	9	process	process	NOUN
cana-3215	43	10	,	,	PUNCT
cana-3215	43	11	except	except	SCONJ
cana-3215	43	12	for	for	ADP
cana-3215	43	13	the	the	DET
cana-3215	43	14	trivial	trivial	ADJ
cana-3215	43	15	loop	loop	NOUN
cana-3215	43	16	(	(	PUNCT
cana-3215	43	17	1	1	NUM
cana-3215	43	18	,	,	PUNCT
cana-3215	43	19	4	4	NUM
cana-3215	43	20	,	,	PUNCT
cana-3215	43	21	2	2	NUM
cana-3215	43	22	,	,	PUNCT
cana-3215	43	23	1	1	NUM
cana-3215	43	24	)	)	PUNCT
cana-3215	43	25	and	and	CCONJ
cana-3215	43	26	no	no	DET
cana-3215	43	27	positive	positive	ADJ
cana-3215	43	28	integer	integer	NOUN
cana-3215	43	29	will	will	AUX
cana-3215	43	30	diverge	diverge	VERB
cana-3215	43	31	to	to	PART
cana-3215	43	32	infinity	infinity	VERB
cana-3215	43	33	.	.	PUNCT
cana-3215	44	1	this	this	PRON
cana-3215	44	2	is	be	AUX
cana-3215	44	3	demonstrated	demonstrate	VERB
cana-3215	44	4	using	use	VERB
cana-3215	44	5	logical	logical	ADJ
cana-3215	44	6	reasoning	reasoning	NOUN
cana-3215	44	7	and	and	CCONJ
cana-3215	44	8	reinforcing	reinforce	VERB
cana-3215	44	9	it	it	PRON
cana-3215	44	10	with	with	ADP
cana-3215	44	11	a	a	DET
cana-3215	44	12	probabilistic	probabilistic	ADJ
cana-3215	44	13	approach	approach	NOUN
cana-3215	44	14	[	[	X
cana-3215	44	15	6	6	NUM
cana-3215	44	16	]	]	PUNCT
cana-3215	44	17	.	.	PUNCT
cana-3215	45	1	the	the	DET
cana-3215	45	2	study	study	NOUN
cana-3215	45	3	[	[	X
cana-3215	45	4	7	7	X
cana-3215	45	5	]	]	X
cana-3215	45	6	aims	aim	VERB
cana-3215	45	7	to	to	PART
cana-3215	45	8	prove	prove	VERB
cana-3215	45	9	the	the	DET
cana-3215	45	10	collatz	collatz	NOUN
cana-3215	45	11	conjecture	conjecture	NOUN
cana-3215	45	12	using	use	VERB
cana-3215	45	13	a	a	DET
cana-3215	45	14	theorem	theorem	ADJ
cana-3215	45	15	-	-	PUNCT
cana-3215	45	16	proving	prove	VERB
cana-3215	45	17	system	system	NOUN
cana-3215	45	18	.	.	PUNCT
cana-3215	46	1	the	the	DET
cana-3215	46	2	approach	approach	NOUN
cana-3215	46	3	includes	include	VERB
cana-3215	46	4	two	two	NUM
cana-3215	46	5	methods	method	NOUN
cana-3215	46	6	a	a	DET
cana-3215	46	7	division	division	NOUN
cana-3215	46	8	sequence	sequence	NOUN
cana-3215	46	9	to	to	PART
cana-3215	46	10	track	track	VERB
cana-3215	46	11	how	how	SCONJ
cana-3215	46	12	many	many	ADJ
cana-3215	46	13	times	time	NOUN
cana-3215	46	14	a	a	DET
cana-3215	46	15	number	number	NOUN
cana-3215	46	16	can	can	AUX
cana-3215	46	17	be	be	AUX
cana-3215	46	18	divided	divide	VERB
cana-3215	46	19	by	by	ADP
cana-3215	46	20	2	2	NUM
cana-3215	46	21	and	and	CCONJ
cana-3215	46	22	a	a	DET
cana-3215	46	23	start	start	NOUN
cana-3215	46	24	conversion	conversion	NOUN
cana-3215	46	25	to	to	PART
cana-3215	46	26	map	map	VERB
cana-3215	46	27	one	one	NUM
cana-3215	46	28	division	division	NOUN
cana-3215	46	29	sequence	sequence	NOUN
cana-3215	46	30	to	to	ADP
cana-3215	46	31	another	another	PRON
cana-3215	46	32	.	.	PUNCT
cana-3215	47	1	methodology	methodology	NOUN
cana-3215	47	2	:	:	PUNCT
cana-3215	47	3	in	in	ADP
cana-3215	47	4	this	this	DET
cana-3215	47	5	paper	paper	NOUN
cana-3215	47	6	,	,	PUNCT
cana-3215	47	7	we	we	PRON
cana-3215	47	8	provide	provide	VERB
cana-3215	47	9	the	the	DET
cana-3215	47	10	proof	proof	NOUN
cana-3215	47	11	of	of	ADP
cana-3215	47	12	the	the	DET
cana-3215	47	13	collatz	collatz	NOUN
cana-3215	47	14	conjecture	conjecture	NOUN
cana-3215	47	15	by	by	ADP
cana-3215	47	16	plotting	plot	VERB
cana-3215	47	17	ananta	ananta	NOUN
cana-3215	47	18	-	-	PUNCT
cana-3215	47	19	graphs	graph	NOUN
cana-3215	47	20	,	,	PUNCT
cana-3215	47	21	a	a	DET
cana-3215	47	22	graphical	graphical	ADJ
cana-3215	47	23	representation	representation	NOUN
cana-3215	47	24	of	of	ADP
cana-3215	47	25	the	the	DET
cana-3215	47	26	collatz	collatz	NOUN
cana-3215	47	27	sequence	sequence	NOUN
cana-3215	47	28	.	.	PUNCT
cana-3215	48	1	computations	computation	NOUN
cana-3215	48	2	to	to	PART
cana-3215	48	3	generate	generate	VERB
cana-3215	48	4	ananta	ananta	NOUN
cana-3215	48	5	-	-	PUNCT
cana-3215	48	6	graph	graph	NOUN
cana-3215	48	7	:	:	PUNCT
cana-3215	48	8	the	the	DET
cana-3215	48	9	program	program	NOUN
cana-3215	48	10	generates	generate	VERB
cana-3215	48	11	a	a	DET
cana-3215	48	12	graph	graph	NOUN
cana-3215	48	13	based	base	VERB
cana-3215	48	14	on	on	ADP
cana-3215	48	15	the	the	DET
cana-3215	48	16	collatz	collatz	NOUN
cana-3215	48	17	conjecture	conjecture	NOUN
cana-3215	48	18	for	for	ADP
cana-3215	48	19	a	a	DET
cana-3215	48	20	given	give	VERB
cana-3215	48	21	number	number	NOUN
cana-3215	48	22	.	.	PUNCT
cana-3215	49	1	it	it	PRON
cana-3215	49	2	includes	include	VERB
cana-3215	49	3	a	a	DET
cana-3215	49	4	function	function	NOUN
cana-3215	49	5	to	to	PART
cana-3215	49	6	convert	convert	VERB
cana-3215	49	7	negative	negative	ADJ
cana-3215	49	8	numbers	number	NOUN
cana-3215	49	9	to	to	ADP
cana-3215	49	10	two	two	NUM
cana-3215	49	11	’s	’s	PART
cana-3215	49	12	complement	complement	NOUN
cana-3215	49	13	,	,	PUNCT
cana-3215	49	14	calculates	calculate	VERB
cana-3215	49	15	the	the	DET
cana-3215	49	16	collatz	collatz	NOUN
cana-3215	49	17	sequence	sequence	NOUN
cana-3215	49	18	until	until	SCONJ
cana-3215	49	19	the	the	DET
cana-3215	49	20	number	number	NOUN
cana-3215	49	21	4	4	NUM
cana-3215	49	22	appears	appear	VERB
cana-3215	49	23	twice	twice	ADV
cana-3215	49	24	and	and	CCONJ
cana-3215	49	25	then	then	ADV
cana-3215	49	26	creates	create	VERB
cana-3215	49	27	a	a	DET
cana-3215	49	28	visual	visual	ADJ
cana-3215	49	29	graph	graph	NOUN
cana-3215	49	30	of	of	ADP
cana-3215	49	31	the	the	DET
cana-3215	49	32	sequence	sequence	NOUN
cana-3215	49	33	.	.	PUNCT
cana-3215	50	1	the	the	DET
cana-3215	50	2	graph	graph	NOUN
cana-3215	50	3	is	be	AUX
cana-3215	50	4	displayed	display	VERB
cana-3215	50	5	using	use	VERB
cana-3215	50	6	matplotlib	matplotlib	PROPN
cana-3215	50	7	and	and	CCONJ
cana-3215	50	8	the	the	DET
cana-3215	50	9	sequence	sequence	NOUN
cana-3215	50	10	can	can	AUX
cana-3215	50	11	be	be	AUX
cana-3215	50	12	shown	show	VERB
cana-3215	50	13	in	in	ADP
cana-3215	50	14	a	a	DET
cana-3215	50	15	table	table	NOUN
cana-3215	50	16	or	or	CCONJ
cana-3215	50	17	exported	export	VERB
cana-3215	50	18	to	to	ADP
cana-3215	50	19	an	an	DET
cana-3215	50	20	excel	excel	NOUN
cana-3215	50	21	file	file	NOUN
cana-3215	50	22	.	.	PUNCT
cana-3215	51	1	a	a	DET
cana-3215	51	2	graphical	graphical	ADJ
cana-3215	51	3	user	user	NOUN
cana-3215	51	4	interface	interface	NOUN
cana-3215	51	5	(	(	PUNCT
cana-3215	51	6	gui	gui	NOUN
cana-3215	51	7	)	)	PUNCT
cana-3215	51	8	built	build	VERB
cana-3215	51	9	with	with	ADP
cana-3215	51	10	tkinter	tkinter	NOUN
cana-3215	51	11	allows	allow	VERB
cana-3215	51	12	the	the	DET
cana-3215	51	13	user	user	NOUN
cana-3215	51	14	to	to	PART
cana-3215	51	15	input	input	VERB
cana-3215	51	16	a	a	DET
cana-3215	51	17	number	number	NOUN
cana-3215	51	18	,	,	PUNCT
cana-3215	51	19	generate	generate	VERB
cana-3215	51	20	the	the	DET
cana-3215	51	21	graph	graph	NOUN
cana-3215	51	22	,	,	PUNCT
cana-3215	51	23	view	view	VERB
cana-3215	51	24	the	the	DET
cana-3215	51	25	sequence	sequence	NOUN
cana-3215	51	26	in	in	ADP
cana-3215	51	27	a	a	DET
cana-3215	51	28	table	table	NOUN
cana-3215	51	29	and	and	CCONJ
cana-3215	51	30	export	export	VERB
cana-3215	51	31	the	the	DET
cana-3215	51	32	data	datum	NOUN
cana-3215	51	33	.	.	PUNCT
cana-3215	52	1	the	the	DET
cana-3215	52	2	gui	gui	NOUN
cana-3215	52	3	features	feature	VERB
cana-3215	52	4	buttons	button	NOUN
cana-3215	52	5	for	for	ADP
cana-3215	52	6	generating	generate	VERB
cana-3215	52	7	the	the	DET
cana-3215	52	8	graph	graph	NOUN
cana-3215	52	9	and	and	CCONJ
cana-3215	52	10	exporting	export	VERB
cana-3215	52	11	the	the	DET
cana-3215	52	12	sequence	sequence	NOUN
cana-3215	52	13	to	to	PART
cana-3215	52	14	excel	excel	VERB
cana-3215	52	15	,	,	PUNCT
cana-3215	52	16	as	as	ADV
cana-3215	52	17	well	well	ADV
cana-3215	52	18	as	as	ADP
cana-3215	52	19	error	error	NOUN
cana-3215	52	20	handling	handling	NOUN
cana-3215	52	21	for	for	ADP
cana-3215	52	22	invalid	invalid	ADJ
cana-3215	52	23	inputs	input	NOUN
cana-3215	52	24	.	.	PUNCT
cana-3215	53	1	below	below	ADV
cana-3215	53	2	are	be	AUX
cana-3215	53	3	the	the	DET
cana-3215	53	4	functions	function	NOUN
cana-3215	53	5	called	call	VERB
cana-3215	53	6	for	for	ADP
cana-3215	53	7	the	the	DET
cana-3215	53	8	same	same	ADJ
cana-3215	53	9	process	process	NOUN
cana-3215	53	10	.	.	PUNCT
cana-3215	54	1	communications	communication	NOUN
cana-3215	54	2	on	on	ADP
cana-3215	54	3	applied	apply	VERB
cana-3215	54	4	nonlinear	nonlinear	ADJ
cana-3215	54	5	analysis	analysis	NOUN
cana-3215	54	6	issn	issn	NOUN
cana-3215	54	7	:	:	PUNCT
cana-3215	54	8	1074	1074	NUM
cana-3215	54	9	-	-	PUNCT
cana-3215	54	10	133x	133x	NUM
cana-3215	54	11	vol	vol	NOUN
cana-3215	54	12	32	32	NUM
cana-3215	54	13	no	no	NOUN
cana-3215	54	14	.	.	PUNCT
cana-3215	55	1	6s	6s	NUM
cana-3215	55	2	(	(	PUNCT
cana-3215	55	3	2025	2025	NUM
cana-3215	55	4	)	)	PUNCT
cana-3215	55	5	19	19	NUM
cana-3215	55	6	https://internationalpubls.com	https://internationalpubls.com	SYM
cana-3215	55	7	•	•	NUM
cana-3215	55	8	twos_complement	twos_complement	NOUN
cana-3215	55	9	function	function	NOUN
cana-3215	55	10	:	:	PUNCT
cana-3215	55	11	this	this	DET
cana-3215	55	12	function	function	NOUN
cana-3215	55	13	handles	handle	VERB
cana-3215	55	14	negative	negative	ADJ
cana-3215	55	15	integers	integer	NOUN
cana-3215	55	16	by	by	ADP
cana-3215	55	17	converting	convert	VERB
cana-3215	55	18	them	they	PRON
cana-3215	55	19	to	to	ADP
cana-3215	55	20	their	their	PRON
cana-3215	55	21	two	two	NUM
cana-3215	55	22	’s	’s	PART
cana-3215	55	23	complement	complement	NOUN
cana-3215	55	24	representation	representation	NOUN
cana-3215	55	25	using	use	VERB
cana-3215	55	26	8	8	NUM
cana-3215	55	27	-	-	PUNCT
cana-3215	55	28	bit	bit	NOUN
cana-3215	55	29	format	format	NOUN
cana-3215	55	30	(	(	PUNCT
cana-3215	55	31	i.e.	i.e.	X
cana-3215	55	32	,	,	PUNCT
cana-3215	55	33	by	by	ADP
cana-3215	55	34	adding	add	VERB
cana-3215	55	35	256	256	NUM
cana-3215	55	36	for	for	ADP
cana-3215	55	37	negative	negative	ADJ
cana-3215	55	38	numbers	number	NOUN
cana-3215	55	39	)	)	PUNCT
cana-3215	55	40	.	.	PUNCT
cana-3215	56	1	if	if	SCONJ
cana-3215	56	2	the	the	DET
cana-3215	56	3	number	number	NOUN
cana-3215	56	4	is	be	AUX
cana-3215	56	5	positive	positive	ADJ
cana-3215	56	6	,	,	PUNCT
cana-3215	56	7	it	it	PRON
cana-3215	56	8	remains	remain	VERB
cana-3215	56	9	unchanged	unchanged	ADJ
cana-3215	56	10	.	.	PUNCT
cana-3215	57	1	•	•	NUM
cana-3215	57	2	collatz_conjecture	collatz_conjecture	NOUN
cana-3215	57	3	function	function	NOUN
cana-3215	57	4	:	:	PUNCT
cana-3215	57	5	this	this	DET
cana-3215	57	6	function	function	NOUN
cana-3215	57	7	generates	generate	VERB
cana-3215	57	8	the	the	DET
cana-3215	57	9	collatz	collatz	NOUN
cana-3215	57	10	sequence	sequence	NOUN
cana-3215	57	11	starting	start	VERB
cana-3215	57	12	from	from	ADP
cana-3215	57	13	a	a	DET
cana-3215	57	14	given	give	VERB
cana-3215	57	15	number	number	NOUN
cana-3215	57	16	.	.	PUNCT
cana-3215	58	1	it	it	PRON
cana-3215	58	2	continues	continue	VERB
cana-3215	58	3	until	until	SCONJ
cana-3215	58	4	the	the	DET
cana-3215	58	5	number	number	NOUN
cana-3215	58	6	4	4	NUM
cana-3215	58	7	appears	appear	VERB
cana-3215	58	8	twice	twice	ADV
cana-3215	58	9	.	.	PUNCT
cana-3215	59	1	if	if	SCONJ
cana-3215	59	2	the	the	DET
cana-3215	59	3	sequence	sequence	NOUN
cana-3215	59	4	is	be	AUX
cana-3215	59	5	long	long	ADJ
cana-3215	59	6	,	,	PUNCT
cana-3215	59	7	it	it	PRON
cana-3215	59	8	truncates	truncate	VERB
cana-3215	59	9	the	the	DET
cana-3215	59	10	middle	middle	ADJ
cana-3215	59	11	part	part	NOUN
cana-3215	59	12	and	and	CCONJ
cana-3215	59	13	inserts	insert	NOUN
cana-3215	59	14	ellipse	ellipse	NOUN
cana-3215	59	15	to	to	PART
cana-3215	59	16	simplify	simplify	VERB
cana-3215	59	17	the	the	DET
cana-3215	59	18	output	output	NOUN
cana-3215	59	19	.	.	PUNCT
cana-3215	60	1	•	•	NUM
cana-3215	60	2	ananta_graph	ananta_graph	PROPN
cana-3215	60	3	function	function	NOUN
cana-3215	60	4	:	:	PUNCT
cana-3215	60	5	this	this	DET
cana-3215	60	6	function	function	NOUN
cana-3215	60	7	creates	create	VERB
cana-3215	60	8	a	a	DET
cana-3215	60	9	graph	graph	NOUN
cana-3215	60	10	representing	represent	VERB
cana-3215	60	11	the	the	DET
cana-3215	60	12	collatz	collatz	NOUN
cana-3215	60	13	sequence	sequence	NOUN
cana-3215	60	14	.	.	PUNCT
cana-3215	61	1	it	it	PRON
cana-3215	61	2	takes	take	VERB
cana-3215	61	3	the	the	DET
cana-3215	61	4	number	number	NOUN
cana-3215	61	5	as	as	ADP
cana-3215	61	6	input	input	NOUN
cana-3215	61	7	.	.	PUNCT
cana-3215	62	1	generates	generate	VERB
cana-3215	62	2	the	the	DET
cana-3215	62	3	sequence	sequence	NOUN
cana-3215	62	4	and	and	CCONJ
cana-3215	62	5	creates	create	VERB
cana-3215	62	6	a	a	DET
cana-3215	62	7	graph	graph	NOUN
cana-3215	62	8	where	where	SCONJ
cana-3215	62	9	each	each	DET
cana-3215	62	10	step	step	NOUN
cana-3215	62	11	in	in	ADP
cana-3215	62	12	the	the	DET
cana-3215	62	13	sequence	sequence	NOUN
cana-3215	62	14	is	be	AUX
cana-3215	62	15	a	a	DET
cana-3215	62	16	node	node	NOUN
cana-3215	62	17	and	and	CCONJ
cana-3215	62	18	the	the	DET
cana-3215	62	19	transitions	transition	NOUN
cana-3215	62	20	between	between	ADP
cana-3215	62	21	numbers	number	NOUN
cana-3215	62	22	are	be	AUX
cana-3215	62	23	the	the	DET
cana-3215	62	24	edges	edge	NOUN
cana-3215	62	25	.	.	PUNCT
cana-3215	63	1	it	it	PRON
cana-3215	63	2	visualizes	visualize	VERB
cana-3215	63	3	and	and	CCONJ
cana-3215	63	4	saves	save	VERB
cana-3215	63	5	the	the	DET
cana-3215	63	6	graph	graph	NOUN
cana-3215	63	7	using	use	VERB
cana-3215	63	8	matplotlib	matplotlib	PROPN
cana-3215	63	9	.	.	PUNCT
cana-3215	64	1	this	this	DET
cana-3215	64	2	function	function	NOUN
cana-3215	64	3	is	be	AUX
cana-3215	64	4	triggered	trigger	VERB
cana-3215	64	5	when	when	SCONJ
cana-3215	64	6	the	the	DET
cana-3215	64	7	user	user	NOUN
cana-3215	64	8	inputs	input	VERB
cana-3215	64	9	a	a	DET
cana-3215	64	10	number	number	NOUN
cana-3215	64	11	and	and	CCONJ
cana-3215	64	12	selects	select	VERB
cana-3215	64	13	a	a	DET
cana-3215	64	14	button	button	NOUN
cana-3215	64	15	in	in	ADP
cana-3215	64	16	the	the	DET
cana-3215	64	17	gui	gui	NOUN
cana-3215	64	18	.	.	PROPN
cana-3215	64	19	•	•	NUM
cana-3215	64	20	display_sequence_table	display_sequence_table	ADJ
cana-3215	64	21	function	function	NOUN
cana-3215	64	22	:	:	PUNCT
cana-3215	64	23	this	this	DET
cana-3215	64	24	function	function	NOUN
cana-3215	64	25	takes	take	VERB
cana-3215	64	26	the	the	DET
cana-3215	64	27	number	number	NOUN
cana-3215	64	28	,	,	PUNCT
cana-3215	64	29	generates	generate	VERB
cana-3215	64	30	the	the	DET
cana-3215	64	31	graph	graph	NOUN
cana-3215	64	32	and	and	CCONJ
cana-3215	64	33	displays	display	VERB
cana-3215	64	34	the	the	DET
cana-3215	64	35	corresponding	corresponding	ADJ
cana-3215	64	36	collatz	collatz	NOUN
cana-3215	64	37	sequence	sequence	NOUN
cana-3215	64	38	in	in	ADP
cana-3215	64	39	a	a	DET
cana-3215	64	40	table	table	NOUN
cana-3215	64	41	.	.	PUNCT
cana-3215	65	1	if	if	SCONJ
cana-3215	65	2	the	the	DET
cana-3215	65	3	input	input	NOUN
cana-3215	65	4	is	be	AUX
cana-3215	65	5	invalid	invalid	ADJ
cana-3215	65	6	,	,	PUNCT
cana-3215	65	7	it	it	PRON
cana-3215	65	8	shows	show	VERB
cana-3215	65	9	an	an	DET
cana-3215	65	10	error	error	NOUN
cana-3215	65	11	message	message	NOUN
cana-3215	65	12	.	.	PUNCT
cana-3215	66	1	this	this	DET
cana-3215	66	2	function	function	NOUN
cana-3215	66	3	is	be	AUX
cana-3215	66	4	responsible	responsible	ADJ
cana-3215	66	5	for	for	ADP
cana-3215	66	6	clearing	clear	VERB
cana-3215	66	7	any	any	DET
cana-3215	66	8	previous	previous	ADJ
cana-3215	66	9	data	datum	NOUN
cana-3215	66	10	from	from	ADP
cana-3215	66	11	the	the	DET
cana-3215	66	12	table	table	NOUN
cana-3215	66	13	and	and	CCONJ
cana-3215	66	14	inserting	insert	VERB
cana-3215	66	15	the	the	DET
cana-3215	66	16	collatz	collatz	NOUN
cana-3215	66	17	sequence	sequence	NOUN
cana-3215	66	18	values	value	NOUN
cana-3215	66	19	into	into	ADP
cana-3215	66	20	the	the	DET
cana-3215	66	21	table	table	NOUN
cana-3215	66	22	along	along	ADP
cana-3215	66	23	with	with	ADP
cana-3215	66	24	their	their	PRON
cana-3215	66	25	step	step	NOUN
cana-3215	66	26	numbers	number	NOUN
cana-3215	66	27	.	.	PUNCT
cana-3215	67	1	•	•	NUM
cana-3215	67	2	export_to_excel	export_to_excel	PROPN
cana-3215	67	3	function	function	NOUN
cana-3215	67	4	:	:	PUNCT
cana-3215	67	5	this	this	DET
cana-3215	67	6	function	function	NOUN
cana-3215	67	7	exports	export	VERB
cana-3215	67	8	the	the	DET
cana-3215	67	9	collatz	collatz	NOUN
cana-3215	67	10	sequence	sequence	NOUN
cana-3215	67	11	to	to	ADP
cana-3215	67	12	an	an	DET
cana-3215	67	13	excel	excel	NOUN
cana-3215	67	14	file	file	NOUN
cana-3215	67	15	when	when	SCONJ
cana-3215	67	16	it	it	PRON
cana-3215	67	17	is	be	AUX
cana-3215	67	18	triggered	trigger	VERB
cana-3215	67	19	after	after	ADP
cana-3215	67	20	generating	generate	VERB
cana-3215	67	21	the	the	DET
cana-3215	67	22	graph	graph	NOUN
cana-3215	67	23	.	.	PUNCT
cana-3215	68	1	it	it	PRON
cana-3215	68	2	handles	handle	VERB
cana-3215	68	3	the	the	DET
cana-3215	68	4	export	export	NOUN
cana-3215	68	5	process	process	NOUN
cana-3215	68	6	only	only	ADV
cana-3215	68	7	if	if	SCONJ
cana-3215	68	8	a	a	DET
cana-3215	68	9	valid	valid	ADJ
cana-3215	68	10	number	number	NOUN
cana-3215	68	11	is	be	AUX
cana-3215	68	12	entered	enter	VERB
cana-3215	68	13	.	.	PUNCT
cana-3215	69	1	•	•	NUM
cana-3215	69	2	create	create	PROPN
cana-3215	69	3	gui	gui	NOUN
cana-3215	69	4	:	:	PUNCT
cana-3215	69	5	this	this	PRON
cana-3215	69	6	sets	set	VERB
cana-3215	69	7	up	up	ADP
cana-3215	69	8	the	the	DET
cana-3215	69	9	graphical	graphical	ADJ
cana-3215	69	10	user	user	NOUN
cana-3215	69	11	interface	interface	NOUN
cana-3215	69	12	using	use	VERB
cana-3215	69	13	tkinter	tkinter	NOUN
cana-3215	69	14	.	.	PUNCT
cana-3215	70	1	it	it	PRON
cana-3215	70	2	includes	include	VERB
cana-3215	70	3	input	input	NOUN
cana-3215	70	4	fields	field	NOUN
cana-3215	70	5	for	for	ADP
cana-3215	70	6	entering	enter	VERB
cana-3215	70	7	a	a	DET
cana-3215	70	8	number	number	NOUN
cana-3215	70	9	,	,	PUNCT
cana-3215	70	10	buttons	button	NOUN
cana-3215	70	11	for	for	ADP
cana-3215	70	12	generating	generate	VERB
cana-3215	70	13	the	the	DET
cana-3215	70	14	graph	graph	NOUN
cana-3215	70	15	and	and	CCONJ
cana-3215	70	16	exporting	export	VERB
cana-3215	70	17	data	datum	NOUN
cana-3215	70	18	and	and	CCONJ
cana-3215	70	19	table	table	NOUN
cana-3215	70	20	to	to	PART
cana-3215	70	21	display	display	VERB
cana-3215	70	22	the	the	DET
cana-3215	70	23	sequence	sequence	NOUN
cana-3215	70	24	.	.	PUNCT
cana-3215	71	1	based	base	VERB
cana-3215	71	2	on	on	ADP
cana-3215	71	3	user	user	NOUN
cana-3215	71	4	actions	action	NOUN
cana-3215	71	5	,	,	PUNCT
cana-3215	71	6	it	it	PRON
cana-3215	71	7	runs	run	VERB
cana-3215	71	8	the	the	DET
cana-3215	71	9	application	application	NOUN
cana-3215	71	10	.	.	PUNCT
cana-3215	72	1	algorithm	algorithm	PROPN
cana-3215	72	2	for	for	ADP
cana-3215	72	3	ananta	ananta	NOUN
cana-3215	72	4	-	-	PUNCT
cana-3215	72	5	graph	graph	NOUN
cana-3215	72	6	generator	generator	NOUN
cana-3215	72	7	:	:	PUNCT
cana-3215	72	8	input	input	NOUN
cana-3215	72	9	:	:	PUNCT
cana-3215	72	10	•	•	ADP
cana-3215	72	11	a	a	DET
cana-3215	72	12	user	user	NOUN
cana-3215	72	13	-	-	PUNCT
cana-3215	72	14	provided	provide	VERB
cana-3215	72	15	integer	integer	NOUN
cana-3215	72	16	n.	n.	NOUN
cana-3215	72	17	output	output	NOUN
cana-3215	72	18	:	:	PUNCT
cana-3215	72	19	•	•	NUM
cana-3215	72	20	visualization	visualization	NOUN
cana-3215	72	21	of	of	ADP
cana-3215	72	22	the	the	DET
cana-3215	72	23	collatz	collatz	NOUN
cana-3215	72	24	sequence	sequence	NOUN
cana-3215	72	25	as	as	ADP
cana-3215	72	26	an	an	DET
cana-3215	72	27	ananta	ananta	NOUN
cana-3215	72	28	-	-	PUNCT
cana-3215	72	29	graph	graph	NOUN
cana-3215	72	30	.	.	PUNCT
cana-3215	73	1	•	•	NUM
cana-3215	73	2	display	display	NOUN
cana-3215	73	3	of	of	ADP
cana-3215	73	4	the	the	DET
cana-3215	73	5	collatz	collatz	NOUN
cana-3215	73	6	sequence	sequence	NOUN
cana-3215	73	7	in	in	ADP
cana-3215	73	8	the	the	DET
cana-3215	73	9	table	table	NOUN
cana-3215	73	10	.	.	PUNCT
cana-3215	74	1	•	•	NOUN
cana-3215	74	2	export	export	VERB
cana-3215	74	3	the	the	DET
cana-3215	74	4	sequence	sequence	NOUN
cana-3215	74	5	to	to	ADP
cana-3215	74	6	an	an	DET
cana-3215	74	7	excel	excel	NOUN
cana-3215	74	8	file	file	NOUN
cana-3215	74	9	.	.	PUNCT
cana-3215	75	1	steps	step	NOUN
cana-3215	75	2	:	:	PUNCT
cana-3215	75	3	1	1	X
cana-3215	75	4	.	.	X
cana-3215	75	5	initialize	initialize	VERB
cana-3215	75	6	the	the	DET
cana-3215	75	7	gui	gui	NOUN
cana-3215	75	8	:	:	PUNCT
cana-3215	75	9	•	•	NOUN
cana-3215	75	10	create	create	VERB
cana-3215	75	11	the	the	DET
cana-3215	75	12	main	main	ADJ
cana-3215	75	13	gui	gui	NOUN
cana-3215	75	14	window	window	NOUN
cana-3215	75	15	using	use	VERB
cana-3215	75	16	the	the	DET
cana-3215	75	17	tkinter	tkinter	NOUN
cana-3215	75	18	library	library	NOUN
cana-3215	75	19	.	.	PUNCT
cana-3215	76	1	•	•	NUM
cana-3215	76	2	add	add	VERB
cana-3215	76	3	widgets	widget	NOUN
cana-3215	76	4	for	for	ADP
cana-3215	76	5	user	user	NOUN
cana-3215	76	6	input	input	NOUN
cana-3215	76	7	(	(	PUNCT
cana-3215	76	8	entry	entry	NOUN
cana-3215	76	9	)	)	PUNCT
cana-3215	76	10	,	,	PUNCT
cana-3215	76	11	buttons	button	NOUN
cana-3215	76	12	,	,	PUNCT
cana-3215	76	13	and	and	CCONJ
cana-3215	76	14	a	a	DET
cana-3215	76	15	table	table	NOUN
cana-3215	76	16	(	(	PUNCT
cana-3215	76	17	treeview	treeview	NOUN
cana-3215	76	18	)	)	PUNCT
cana-3215	76	19	to	to	PART
cana-3215	76	20	display	display	VERB
cana-3215	76	21	results	result	NOUN
cana-3215	76	22	.	.	PUNCT
cana-3215	77	1	2	2	X
cana-3215	77	2	.	.	X
cana-3215	77	3	two	two	NUM
cana-3215	77	4	’s	’s	PART
cana-3215	77	5	complement	complement	NOUN
cana-3215	77	6	conversion	conversion	NOUN
cana-3215	77	7	function	function	NOUN
cana-3215	77	8	(	(	PUNCT
cana-3215	77	9	twos_complement	twos_complement	NOUN
cana-3215	77	10	):	):	PUNCT
cana-3215	77	11	•	•	ADP
cana-3215	77	12	if	if	SCONJ
cana-3215	77	13	n	n	PRON
cana-3215	77	14	is	be	AUX
cana-3215	77	15	negative	negative	ADJ
cana-3215	77	16	,	,	PUNCT
cana-3215	77	17	convert	convert	VERB
cana-3215	77	18	it	it	PRON
cana-3215	77	19	to	to	ADP
cana-3215	77	20	its	its	PRON
cana-3215	77	21	two	two	NUM
cana-3215	77	22	’s	’s	PART
cana-3215	77	23	complement	complement	NOUN
cana-3215	77	24	representation	representation	NOUN
cana-3215	77	25	for	for	ADP
cana-3215	77	26	an	an	DET
cana-3215	77	27	8	8	NUM
cana-3215	77	28	-	-	PUNCT
cana-3215	77	29	bit	bit	NOUN
cana-3215	77	30	number	number	NOUN
cana-3215	77	31	.	.	PUNCT
cana-3215	78	1	3	3	X
cana-3215	78	2	.	.	X
cana-3215	78	3	collatz	collatz	NOUN
cana-3215	78	4	conjecture	conjecture	VERB
cana-3215	78	5	function	function	NOUN
cana-3215	78	6	(	(	PUNCT
cana-3215	78	7	collatz_conjecture	collatz_conjecture	NOUN
cana-3215	78	8	):	):	PUNCT
cana-3215	78	9	•	•	ADP
cana-3215	78	10	start	start	VERB
cana-3215	78	11	with	with	ADP
cana-3215	78	12	the	the	DET
cana-3215	78	13	input	input	NOUN
cana-3215	78	14	number	number	NOUN
cana-3215	78	15	n.	n.	NOUN
cana-3215	78	16	•	•	PUNCT
cana-3215	78	17	generate	generate	VERB
cana-3215	78	18	the	the	DET
cana-3215	78	19	sequence	sequence	NOUN
cana-3215	78	20	by	by	ADP
cana-3215	78	21	:	:	PUNCT
cana-3215	78	22	o	o	NOUN
cana-3215	78	23	dividing	divide	VERB
cana-3215	78	24	n	n	INTJ
cana-3215	78	25	by	by	ADP
cana-3215	78	26	2	2	NUM
cana-3215	78	27	if	if	SCONJ
cana-3215	78	28	even	even	ADV
cana-3215	78	29	.	.	PUNCT
cana-3215	79	1	o	o	X
cana-3215	79	2	multiplying	multiplying	NOUN
cana-3215	79	3	n	n	NOUN
cana-3215	79	4	by	by	ADP
cana-3215	79	5	3	3	NUM
cana-3215	79	6	and	and	CCONJ
cana-3215	79	7	adding	add	VERB
cana-3215	79	8	1	1	NUM
cana-3215	79	9	if	if	SCONJ
cana-3215	79	10	odd	odd	ADJ
cana-3215	79	11	.	.	PUNCT
cana-3215	80	1	•	•	NUM
cana-3215	80	2	stop	stop	VERB
cana-3215	80	3	when	when	SCONJ
cana-3215	80	4	the	the	DET
cana-3215	80	5	number	number	NOUN
cana-3215	80	6	4	4	NUM
cana-3215	80	7	appears	appear	VERB
cana-3215	80	8	for	for	ADP
cana-3215	80	9	the	the	DET
cana-3215	80	10	second	second	ADJ
cana-3215	80	11	time	time	NOUN
cana-3215	80	12	.	.	PUNCT
cana-3215	81	1	communications	communication	NOUN
cana-3215	81	2	on	on	ADP
cana-3215	81	3	applied	apply	VERB
cana-3215	81	4	nonlinear	nonlinear	ADJ
cana-3215	81	5	analysis	analysis	NOUN
cana-3215	81	6	issn	issn	NOUN
cana-3215	81	7	:	:	PUNCT
cana-3215	81	8	1074	1074	NUM
cana-3215	81	9	-	-	PUNCT
cana-3215	81	10	133x	133x	NUM
cana-3215	81	11	vol	vol	NOUN
cana-3215	81	12	32	32	NUM
cana-3215	81	13	no	no	NOUN
cana-3215	81	14	.	.	PUNCT
cana-3215	82	1	6s	6s	NUM
cana-3215	82	2	(	(	PUNCT
cana-3215	82	3	2025	2025	NUM
cana-3215	82	4	)	)	PUNCT
cana-3215	82	5	20	20	NUM
cana-3215	82	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3215	82	7	•	•	NUM
cana-3215	82	8	append	append	NOUN
cana-3215	82	9	2	2	NUM
cana-3215	82	10	and	and	CCONJ
cana-3215	82	11	1	1	NUM
cana-3215	82	12	to	to	PART
cana-3215	82	13	complete	complete	VERB
cana-3215	82	14	the	the	DET
cana-3215	82	15	sequence	sequence	NOUN
cana-3215	82	16	.	.	PUNCT
cana-3215	83	1	•	•	NUM
cana-3215	83	2	shorten	shorten	VERB
cana-3215	83	3	the	the	DET
cana-3215	83	4	sequence	sequence	NOUN
cana-3215	83	5	if	if	SCONJ
cana-3215	83	6	it	it	PRON
cana-3215	83	7	has	have	VERB
cana-3215	83	8	more	more	ADJ
cana-3215	83	9	than	than	ADP
cana-3215	83	10	20	20	NUM
cana-3215	83	11	elements	element	NOUN
cana-3215	83	12	by	by	ADP
cana-3215	83	13	adding	add	VERB
cana-3215	83	14	placeholders	placeholder	NOUN
cana-3215	83	15	(	(	PUNCT
cana-3215	83	16	“	"	PUNCT
cana-3215	83	17	…	…	PUNCT
cana-3215	83	18	…	…	PUNCT
cana-3215	83	19	.	.	PUNCT
cana-3215	83	20	”	"	PUNCT
cana-3215	83	21	)	)	PUNCT
cana-3215	83	22	.	.	PUNCT
cana-3215	84	1	4	4	X
cana-3215	84	2	.	.	X
cana-3215	84	3	ananta	ananta	NOUN
cana-3215	84	4	-	-	PUNCT
cana-3215	84	5	graph	graph	NOUN
cana-3215	84	6	creation	creation	NOUN
cana-3215	84	7	(	(	PUNCT
cana-3215	84	8	ananta	ananta	NOUN
cana-3215	84	9	-	-	PUNCT
cana-3215	84	10	graph	graph	NOUN
cana-3215	84	11	):	):	PUNCT
cana-3215	84	12	•	•	X
cana-3215	84	13	use	use	VERB
cana-3215	84	14	the	the	DET
cana-3215	84	15	collatz	collatz	NOUN
cana-3215	84	16	sequence	sequence	NOUN
cana-3215	84	17	to	to	PART
cana-3215	84	18	construct	construct	VERB
cana-3215	84	19	a	a	DET
cana-3215	84	20	graph	graph	NOUN
cana-3215	84	21	using	use	VERB
cana-3215	84	22	networkz	networkz	NOUN
cana-3215	84	23	.	.	PUNCT
cana-3215	85	1	•	•	NOUN
cana-3215	85	2	add	add	VERB
cana-3215	85	3	nodes	node	NOUN
cana-3215	85	4	and	and	CCONJ
cana-3215	85	5	edges	edge	NOUN
cana-3215	85	6	between	between	ADP
cana-3215	85	7	consecutive	consecutive	ADJ
cana-3215	85	8	numbers	number	NOUN
cana-3215	85	9	in	in	ADP
cana-3215	85	10	the	the	DET
cana-3215	85	11	sequence	sequence	NOUN
cana-3215	85	12	.	.	PUNCT
cana-3215	86	1	•	•	NUM
cana-3215	86	2	use	use	VERB
cana-3215	86	3	a	a	DET
cana-3215	86	4	linear	linear	ADJ
cana-3215	86	5	layout	layout	NOUN
cana-3215	86	6	to	to	ADP
cana-3215	86	7	position	position	NOUN
cana-3215	86	8	nodes	node	NOUN
cana-3215	86	9	,	,	PUNCT
cana-3215	86	10	with	with	SCONJ
cana-3215	86	11	the	the	DET
cana-3215	86	12	final	final	ADJ
cana-3215	86	13	loop	loop	NOUN
cana-3215	86	14	node	node	NOUN
cana-3215	86	15	placed	place	VERB
cana-3215	86	16	distinctly	distinctly	ADV
cana-3215	86	17	.	.	PUNCT
cana-3215	87	1	•	•	ADV
cana-3215	87	2	save	save	VERB
cana-3215	87	3	and	and	CCONJ
cana-3215	87	4	display	display	VERB
cana-3215	87	5	the	the	DET
cana-3215	87	6	graph	graph	NOUN
cana-3215	87	7	as	as	ADP
cana-3215	87	8	an	an	DET
cana-3215	87	9	image	image	NOUN
cana-3215	87	10	using	use	VERB
cana-3215	87	11	matplotlib	matplotlib	PROPN
cana-3215	87	12	.	.	PUNCT
cana-3215	88	1	5	5	NUM
cana-3215	88	2	.	.	X
cana-3215	88	3	generate	generate	VERB
cana-3215	88	4	graph	graph	NOUN
cana-3215	88	5	and	and	CCONJ
cana-3215	88	6	display	display	NOUN
cana-3215	88	7	sequence	sequence	NOUN
cana-3215	88	8	:	:	PUNCT
cana-3215	88	9	•	•	PUNCT
cana-3215	88	10	retrieve	retrieve	VERB
cana-3215	88	11	the	the	DET
cana-3215	88	12	input	input	NOUN
cana-3215	88	13	number	number	NOUN
cana-3215	88	14	from	from	ADP
cana-3215	88	15	the	the	DET
cana-3215	88	16	gui	gui	NOUN
cana-3215	88	17	entry	entry	NOUN
cana-3215	88	18	field	field	NOUN
cana-3215	88	19	.	.	PUNCT
cana-3215	89	1	•	•	NUM
cana-3215	89	2	compute	compute	VERB
cana-3215	89	3	the	the	DET
cana-3215	89	4	collatz	collatz	NOUN
cana-3215	89	5	sequence	sequence	NOUN
cana-3215	89	6	and	and	CCONJ
cana-3215	89	7	display	display	VERB
cana-3215	89	8	the	the	DET
cana-3215	89	9	graph	graph	NOUN
cana-3215	89	10	.	.	PUNCT
cana-3215	90	1	•	•	NOUN
cana-3215	90	2	display	display	VERB
cana-3215	90	3	the	the	DET
cana-3215	90	4	sequence	sequence	NOUN
cana-3215	90	5	in	in	ADP
cana-3215	90	6	a	a	DET
cana-3215	90	7	table	table	NOUN
cana-3215	90	8	format	format	NOUN
cana-3215	90	9	(	(	PUNCT
cana-3215	90	10	treeview	treeview	NOUN
cana-3215	90	11	)	)	PUNCT
cana-3215	90	12	.	.	PUNCT
cana-3215	91	1	6	6	X
cana-3215	91	2	.	.	X
cana-3215	91	3	export	export	NOUN
cana-3215	91	4	sequence	sequence	NOUN
cana-3215	91	5	to	to	PART
cana-3215	91	6	excel	excel	VERB
cana-3215	91	7	(	(	PUNCT
cana-3215	91	8	export_to_excel	export_to_excel	PROPN
cana-3215	91	9	):	):	PUNCT
cana-3215	91	10	•	•	NUM
cana-3215	91	11	convert	convert	VERB
cana-3215	91	12	the	the	DET
cana-3215	91	13	collatz	collatz	NOUN
cana-3215	91	14	sequence	sequence	NOUN
cana-3215	91	15	into	into	ADP
cana-3215	91	16	a	a	DET
cana-3215	91	17	dataframe	dataframe	ADJ
cana-3215	91	18	using	use	VERB
cana-3215	91	19	pandas	panda	NOUN
cana-3215	91	20	.	.	PUNCT
cana-3215	92	1	•	•	INTJ
cana-3215	92	2	save	save	VERB
cana-3215	92	3	the	the	DET
cana-3215	92	4	dataframe	dataframe	PROPN
cana-3215	92	5	to	to	ADP
cana-3215	92	6	an	an	DET
cana-3215	92	7	excel	excel	NOUN
cana-3215	92	8	file	file	NOUN
cana-3215	92	9	(	(	PUNCT
cana-3215	92	10	collatz_sequence.xlsx	collatz_sequence.xlsx	NOUN
cana-3215	92	11	)	)	PUNCT
cana-3215	92	12	.	.	PUNCT
cana-3215	93	1	•	•	NOUN
cana-3215	93	2	display	display	VERB
cana-3215	93	3	a	a	DET
cana-3215	93	4	success	success	NOUN
cana-3215	93	5	message	message	NOUN
cana-3215	93	6	or	or	CCONJ
cana-3215	93	7	handle	handle	VERB
cana-3215	93	8	errors	error	NOUN
cana-3215	93	9	,	,	PUNCT
cana-3215	93	10	if	if	SCONJ
cana-3215	93	11	any	any	PRON
cana-3215	93	12	.	.	NOUN
cana-3215	93	13	7	7	X
cana-3215	93	14	.	.	X
cana-3215	93	15	gui	gui	NOUN
cana-3215	93	16	interactions	interaction	NOUN
cana-3215	93	17	:	:	PUNCT
cana-3215	93	18	•	•	NOUN
cana-3215	93	19	generate	generate	VERB
cana-3215	93	20	graph	graph	NOUN
cana-3215	93	21	button	button	NOUN
cana-3215	93	22	:	:	PUNCT
cana-3215	93	23	calls	call	VERB
cana-3215	93	24	the	the	DET
cana-3215	93	25	generate_graph	generate_graph	PROPN
cana-3215	93	26	function	function	NOUN
cana-3215	93	27	to	to	PART
cana-3215	93	28	compute	compute	VERB
cana-3215	93	29	the	the	DET
cana-3215	93	30	sequence	sequence	NOUN
cana-3215	93	31	,	,	PUNCT
cana-3215	93	32	display	display	VERB
cana-3215	93	33	the	the	DET
cana-3215	93	34	graph	graph	NOUN
cana-3215	93	35	,	,	PUNCT
cana-3215	93	36	and	and	CCONJ
cana-3215	93	37	populate	populate	VERB
cana-3215	93	38	the	the	DET
cana-3215	93	39	table	table	NOUN
cana-3215	93	40	.	.	PUNCT
cana-3215	94	1	•	•	NOUN
cana-3215	94	2	export	export	NOUN
cana-3215	94	3	to	to	PART
cana-3215	94	4	excel	excel	VERB
cana-3215	94	5	button	button	NOUN
cana-3215	94	6	:	:	PUNCT
cana-3215	95	1	exports	export	NOUN
cana-3215	95	2	the	the	DET
cana-3215	95	3	displayed	displayed	ADJ
cana-3215	95	4	sequence	sequence	NOUN
cana-3215	95	5	to	to	ADP
cana-3215	95	6	an	an	DET
cana-3215	95	7	excel	excel	NOUN
cana-3215	95	8	file	file	NOUN
cana-3215	95	9	.	.	PUNCT
cana-3215	96	1	8	8	NUM
cana-3215	96	2	.	.	X
cana-3215	96	3	error	error	NOUN
cana-3215	96	4	handling	handling	NOUN
cana-3215	96	5	:	:	PUNCT
cana-3215	96	6	•	•	NUM
cana-3215	96	7	display	display	VERB
cana-3215	96	8	appropriate	appropriate	ADJ
cana-3215	96	9	error	error	NOUN
cana-3215	96	10	messages	message	NOUN
cana-3215	96	11	for	for	ADP
cana-3215	96	12	invalid	invalid	ADJ
cana-3215	96	13	inputs	input	NOUN
cana-3215	96	14	or	or	CCONJ
cana-3215	96	15	export	export	NOUN
cana-3215	96	16	errors	error	NOUN
cana-3215	96	17	using	use	VERB
cana-3215	96	18	messagebox	messagebox	NOUN
cana-3215	96	19	.	.	PUNCT
cana-3215	97	1	9	9	NUM
cana-3215	97	2	.	.	X
cana-3215	97	3	display	display	NOUN
cana-3215	97	4	output	output	NOUN
cana-3215	97	5	:	:	PUNCT
cana-3215	97	6	•	•	NUM
cana-3215	97	7	show	show	VERB
cana-3215	97	8	the	the	DET
cana-3215	97	9	ananta	ananta	NOUN
cana-3215	97	10	-	-	PUNCT
cana-3215	97	11	graph	graph	NOUN
cana-3215	97	12	visualization	visualization	NOUN
cana-3215	97	13	and	and	CCONJ
cana-3215	97	14	the	the	DET
cana-3215	97	15	sequence	sequence	NOUN
cana-3215	97	16	table	table	NOUN
cana-3215	97	17	.	.	PUNCT
cana-3215	98	1	•	•	NOUN
cana-3215	98	2	save	save	VERB
cana-3215	98	3	the	the	DET
cana-3215	98	4	sequence	sequence	NOUN
cana-3215	98	5	to	to	PART
cana-3215	98	6	excel	excel	VERB
cana-3215	98	7	.	.	PUNCT
cana-3215	99	1	in	in	ADP
cana-3215	99	2	this	this	DET
cana-3215	99	3	paper	paper	NOUN
cana-3215	99	4	,	,	PUNCT
cana-3215	99	5	we	we	PRON
cana-3215	99	6	generate	generate	VERB
cana-3215	99	7	the	the	DET
cana-3215	99	8	ananta	ananta	NOUN
cana-3215	99	9	-	-	PUNCT
cana-3215	99	10	graph	graph	NOUN
cana-3215	99	11	for	for	ADP
cana-3215	99	12	the	the	DET
cana-3215	99	13	positive	positive	ADJ
cana-3215	99	14	integers	integer	NOUN
cana-3215	99	15	using	use	VERB
cana-3215	99	16	python	python	PROPN
cana-3215	99	17	code	code	NOUN
cana-3215	99	18	based	base	VERB
cana-3215	99	19	on	on	ADP
cana-3215	99	20	the	the	DET
cana-3215	99	21	above	above	ADJ
cana-3215	99	22	pseudocode	pseudocode	NOUN
cana-3215	99	23	.	.	PUNCT
cana-3215	100	1	following	follow	VERB
cana-3215	100	2	are	be	AUX
cana-3215	100	3	some	some	DET
cana-3215	100	4	positive	positive	ADJ
cana-3215	100	5	numbers	number	NOUN
cana-3215	100	6	with	with	ADP
cana-3215	100	7	their	their	PRON
cana-3215	100	8	collatz	collatz	NOUN
cana-3215	100	9	sequence	sequence	NOUN
cana-3215	100	10	and	and	CCONJ
cana-3215	100	11	their	their	PRON
cana-3215	100	12	anantagraph	anantagraph	ADJ
cana-3215	100	13	representation	representation	NOUN
cana-3215	100	14	.	.	PUNCT
cana-3215	101	1	ananta	ananta	NOUN
cana-3215	101	2	-	-	PUNCT
cana-3215	101	3	graphs	graph	NOUN
cana-3215	101	4	with	with	ADP
cana-3215	101	5	sequence	sequence	NOUN
cana-3215	101	6	n=7	n=7	PROPN
cana-3215	101	7	collatz	collatz	NOUN
cana-3215	101	8	sequence	sequence	NOUN
cana-3215	101	9	:	:	PUNCT
cana-3215	101	10	7	7	NUM
cana-3215	101	11	,	,	PUNCT
cana-3215	101	12	22	22	NUM
cana-3215	101	13	,	,	PUNCT
cana-3215	101	14	11	11	NUM
cana-3215	101	15	,	,	PUNCT
cana-3215	101	16	34	34	NUM
cana-3215	101	17	,	,	PUNCT
cana-3215	101	18	17	17	NUM
cana-3215	101	19	,	,	PUNCT
cana-3215	101	20	52	52	NUM
cana-3215	101	21	,	,	PUNCT
cana-3215	101	22	26	26	NUM
cana-3215	101	23	,	,	PUNCT
cana-3215	101	24	13	13	NUM
cana-3215	101	25	,	,	PUNCT
cana-3215	101	26	40	40	NUM
cana-3215	101	27	,	,	PUNCT
cana-3215	101	28	20	20	NUM
cana-3215	101	29	,	,	PUNCT
cana-3215	101	30	10	10	NUM
cana-3215	101	31	,	,	PUNCT
cana-3215	101	32	5	5	NUM
cana-3215	101	33	,	,	PUNCT
cana-3215	101	34	16	16	NUM
cana-3215	101	35	,	,	PUNCT
cana-3215	101	36	8	8	NUM
cana-3215	101	37	,	,	PUNCT
cana-3215	101	38	4	4	NUM
cana-3215	101	39	,	,	PUNCT
cana-3215	101	40	2	2	NUM
cana-3215	101	41	,	,	PUNCT
cana-3215	101	42	1	1	NUM
cana-3215	101	43	,	,	PUNCT
cana-3215	101	44	4	4	NUM
cana-3215	101	45	,	,	PUNCT
cana-3215	101	46	2	2	NUM
cana-3215	101	47	,	,	PUNCT
cana-3215	101	48	1	1	NUM
cana-3215	101	49	n=15	n=15	ADV
cana-3215	101	50	collatz	collatz	NOUN
cana-3215	101	51	sequence	sequence	NOUN
cana-3215	101	52	:	:	PUNCT
cana-3215	101	53	15	15	NUM
cana-3215	101	54	,	,	PUNCT
cana-3215	101	55	46	46	NUM
cana-3215	101	56	,	,	PUNCT
cana-3215	101	57	23	23	NUM
cana-3215	101	58	,	,	PUNCT
cana-3215	101	59	70	70	NUM
cana-3215	101	60	,	,	PUNCT
cana-3215	101	61	35	35	NUM
cana-3215	101	62	,	,	PUNCT
cana-3215	101	63	106	106	NUM
cana-3215	101	64	,	,	PUNCT
cana-3215	101	65	53	53	NUM
cana-3215	101	66	,	,	PUNCT
cana-3215	101	67	160	160	NUM
cana-3215	101	68	,	,	PUNCT
cana-3215	101	69	80	80	NUM
cana-3215	101	70	,	,	PUNCT
cana-3215	101	71	40	40	NUM
cana-3215	101	72	,	,	PUNCT
cana-3215	101	73	20	20	NUM
cana-3215	101	74	,	,	PUNCT
cana-3215	101	75	10	10	NUM
cana-3215	101	76	,	,	PUNCT
cana-3215	101	77	5	5	NUM
cana-3215	101	78	,	,	PUNCT
cana-3215	101	79	16	16	NUM
cana-3215	101	80	,	,	PUNCT
cana-3215	101	81	8	8	NUM
cana-3215	101	82	,	,	PUNCT
cana-3215	101	83	4	4	NUM
cana-3215	101	84	,	,	PUNCT
cana-3215	101	85	2	2	NUM
cana-3215	101	86	,	,	PUNCT
cana-3215	101	87	1	1	NUM
cana-3215	101	88	,	,	PUNCT
cana-3215	101	89	4	4	NUM
cana-3215	101	90	,	,	PUNCT
cana-3215	101	91	2	2	NUM
cana-3215	101	92	,	,	PUNCT
cana-3215	101	93	1	1	NUM
cana-3215	101	94	communications	communication	NOUN
cana-3215	101	95	on	on	ADP
cana-3215	101	96	applied	apply	VERB
cana-3215	101	97	nonlinear	nonlinear	ADJ
cana-3215	101	98	analysis	analysis	NOUN
cana-3215	101	99	issn	issn	NOUN
cana-3215	101	100	:	:	PUNCT
cana-3215	101	101	1074	1074	NUM
cana-3215	101	102	-	-	PUNCT
cana-3215	101	103	133x	133x	NUM
cana-3215	101	104	vol	vol	NOUN
cana-3215	101	105	32	32	NUM
cana-3215	101	106	no	no	NOUN
cana-3215	101	107	.	.	PUNCT
cana-3215	102	1	6s	6s	NUM
cana-3215	102	2	(	(	PUNCT
cana-3215	102	3	2025	2025	NUM
cana-3215	102	4	)	)	PUNCT
cana-3215	102	5	21	21	NUM
cana-3215	102	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3215	102	7	n=37	n=37	PROPN
cana-3215	102	8	collatz	collatz	PROPN
cana-3215	102	9	sequence	sequence	NOUN
cana-3215	102	10	:	:	PUNCT
cana-3215	102	11	37	37	NUM
cana-3215	102	12	,	,	PUNCT
cana-3215	102	13	112	112	NUM
cana-3215	102	14	,	,	PUNCT
cana-3215	102	15	56	56	NUM
cana-3215	102	16	,	,	PUNCT
cana-3215	102	17	28	28	NUM
cana-3215	102	18	,	,	PUNCT
cana-3215	102	19	14	14	NUM
cana-3215	102	20	,	,	PUNCT
cana-3215	102	21	7	7	NUM
cana-3215	102	22	,	,	PUNCT
cana-3215	102	23	22	22	NUM
cana-3215	102	24	,	,	PUNCT
cana-3215	102	25	11	11	NUM
cana-3215	102	26	,	,	PUNCT
cana-3215	102	27	34	34	NUM
cana-3215	102	28	,	,	PUNCT
cana-3215	102	29	17	17	NUM
cana-3215	102	30	,	,	PUNCT
cana-3215	102	31	52	52	NUM
cana-3215	102	32	,	,	PUNCT
cana-3215	102	33	26	26	NUM
cana-3215	102	34	,	,	PUNCT
cana-3215	102	35	13	13	NUM
cana-3215	102	36	,	,	PUNCT
cana-3215	102	37	40	40	NUM
cana-3215	102	38	,	,	PUNCT
cana-3215	102	39	20	20	NUM
cana-3215	102	40	,	,	PUNCT
cana-3215	102	41	10	10	NUM
cana-3215	102	42	,	,	PUNCT
cana-3215	102	43	5	5	NUM
cana-3215	102	44	,	,	PUNCT
cana-3215	102	45	16	16	NUM
cana-3215	102	46	,	,	PUNCT
cana-3215	102	47	8	8	NUM
cana-3215	102	48	,	,	PUNCT
cana-3215	102	49	4	4	NUM
cana-3215	102	50	,	,	PUNCT
cana-3215	102	51	2	2	NUM
cana-3215	102	52	,	,	PUNCT
cana-3215	102	53	1	1	NUM
cana-3215	102	54	,	,	PUNCT
cana-3215	102	55	4	4	NUM
cana-3215	102	56	,	,	PUNCT
cana-3215	102	57	2	2	NUM
cana-3215	102	58	,	,	PUNCT
cana-3215	102	59	1	1	NUM
cana-3215	102	60	n=59	n=59	NOUN
cana-3215	102	61	collatz	collatz	NOUN
cana-3215	102	62	sequence	sequence	NOUN
cana-3215	102	63	:	:	PUNCT
cana-3215	102	64	59	59	NUM
cana-3215	102	65	,	,	PUNCT
cana-3215	102	66	178	178	NUM
cana-3215	102	67	,	,	PUNCT
cana-3215	102	68	89	89	NUM
cana-3215	102	69	,	,	PUNCT
cana-3215	102	70	268	268	NUM
cana-3215	102	71	,	,	PUNCT
cana-3215	102	72	134	134	NUM
cana-3215	102	73	,	,	PUNCT
cana-3215	102	74	67	67	NUM
cana-3215	102	75	,	,	PUNCT
cana-3215	102	76	202	202	NUM
cana-3215	102	77	,	,	PUNCT
cana-3215	102	78	101	101	NUM
cana-3215	102	79	,	,	PUNCT
cana-3215	102	80	304	304	NUM
cana-3215	102	81	,	,	PUNCT
cana-3215	102	82	152	152	NUM
cana-3215	102	83	,	,	PUNCT
cana-3215	102	84	76	76	NUM
cana-3215	102	85	,	,	PUNCT
cana-3215	102	86	38	38	NUM
cana-3215	102	87	,	,	PUNCT
cana-3215	102	88	19	19	NUM
cana-3215	102	89	,	,	PUNCT
cana-3215	102	90	58	58	NUM
cana-3215	102	91	,	,	PUNCT
cana-3215	102	92	29	29	NUM
cana-3215	102	93	,	,	PUNCT
cana-3215	102	94	88	88	NUM
cana-3215	102	95	,	,	PUNCT
cana-3215	102	96	44	44	NUM
cana-3215	102	97	,	,	PUNCT
cana-3215	102	98	22	22	NUM
cana-3215	102	99	,	,	PUNCT
cana-3215	102	100	11	11	NUM
cana-3215	102	101	,	,	PUNCT
cana-3215	102	102	34	34	NUM
cana-3215	102	103	,	,	PUNCT
cana-3215	102	104	17	17	NUM
cana-3215	102	105	,	,	PUNCT
cana-3215	102	106	52	52	NUM
cana-3215	102	107	,	,	PUNCT
cana-3215	102	108	26	26	NUM
cana-3215	102	109	,	,	PUNCT
cana-3215	102	110	13	13	NUM
cana-3215	102	111	,	,	PUNCT
cana-3215	102	112	40	40	NUM
cana-3215	102	113	,	,	PUNCT
cana-3215	102	114	20	20	NUM
cana-3215	102	115	,	,	PUNCT
cana-3215	102	116	10	10	NUM
cana-3215	102	117	,	,	PUNCT
cana-3215	102	118	5	5	NUM
cana-3215	102	119	,	,	PUNCT
cana-3215	102	120	16	16	NUM
cana-3215	102	121	,	,	PUNCT
cana-3215	102	122	8	8	NUM
cana-3215	102	123	,	,	PUNCT
cana-3215	102	124	4	4	NUM
cana-3215	102	125	,	,	PUNCT
cana-3215	102	126	2	2	NUM
cana-3215	102	127	,	,	PUNCT
cana-3215	102	128	1	1	NUM
cana-3215	102	129	,	,	PUNCT
cana-3215	102	130	4	4	NUM
cana-3215	102	131	,	,	PUNCT
cana-3215	102	132	2	2	NUM
cana-3215	102	133	,	,	PUNCT
cana-3215	102	134	1	1	NUM
cana-3215	102	135	n=83	n=83	NOUN
cana-3215	102	136	collatz	collatz	NOUN
cana-3215	102	137	sequence	sequence	NOUN
cana-3215	102	138	:	:	PUNCT
cana-3215	102	139	83	83	NUM
cana-3215	102	140	,	,	PUNCT
cana-3215	102	141	250	250	NUM
cana-3215	102	142	,	,	PUNCT
cana-3215	102	143	125	125	NUM
cana-3215	102	144	,	,	PUNCT
cana-3215	102	145	376	376	NUM
cana-3215	102	146	,	,	PUNCT
cana-3215	102	147	188	188	NUM
cana-3215	102	148	,	,	PUNCT
cana-3215	102	149	94	94	NUM
cana-3215	102	150	,	,	PUNCT
cana-3215	102	151	47	47	NUM
cana-3215	102	152	,	,	PUNCT
cana-3215	102	153	142	142	NUM
cana-3215	102	154	,	,	PUNCT
cana-3215	102	155	71	71	NUM
cana-3215	102	156	,	,	PUNCT
cana-3215	102	157	214	214	NUM
cana-3215	102	158	,	,	PUNCT
cana-3215	102	159	107	107	NUM
cana-3215	102	160	,	,	PUNCT
cana-3215	102	161	322	322	NUM
cana-3215	102	162	,	,	PUNCT
cana-3215	102	163	161	161	NUM
cana-3215	102	164	,	,	PUNCT
cana-3215	102	165	484	484	NUM
cana-3215	102	166	,	,	PUNCT
cana-3215	102	167	242	242	NUM
cana-3215	102	168	,	,	PUNCT
cana-3215	102	169	121	121	NUM
cana-3215	102	170	,	,	PUNCT
cana-3215	102	171	364	364	NUM
cana-3215	102	172	,	,	PUNCT
cana-3215	102	173	182	182	NUM
cana-3215	102	174	,	,	PUNCT
cana-3215	102	175	91	91	NUM
cana-3215	102	176	,	,	PUNCT
cana-3215	102	177	274	274	NUM
cana-3215	102	178	,	,	PUNCT
cana-3215	102	179	137	137	NUM
cana-3215	102	180	,	,	PUNCT
cana-3215	102	181	412	412	NUM
cana-3215	102	182	,	,	PUNCT
cana-3215	102	183	206	206	NUM
cana-3215	102	184	,	,	PUNCT
cana-3215	102	185	103	103	NUM
cana-3215	102	186	,	,	PUNCT
cana-3215	102	187	310	310	NUM
cana-3215	102	188	,	,	PUNCT
cana-3215	102	189	155	155	NUM
cana-3215	102	190	,	,	PUNCT
cana-3215	102	191	466	466	NUM
cana-3215	102	192	,	,	PUNCT
cana-3215	102	193	233	233	NUM
cana-3215	102	194	,	,	PUNCT
cana-3215	102	195	700	700	NUM
cana-3215	102	196	,	,	PUNCT
cana-3215	102	197	350	350	NUM
cana-3215	102	198	,	,	PUNCT
cana-3215	102	199	175	175	NUM
cana-3215	102	200	,	,	PUNCT
cana-3215	102	201	526	526	NUM
cana-3215	102	202	,	,	PUNCT
cana-3215	102	203	263	263	NUM
cana-3215	102	204	,	,	PUNCT
cana-3215	102	205	790	790	NUM
cana-3215	102	206	,	,	PUNCT
cana-3215	102	207	395	395	NUM
cana-3215	102	208	,	,	PUNCT
cana-3215	102	209	1186	1186	NUM
cana-3215	102	210	,	,	PUNCT
cana-3215	102	211	593	593	NUM
cana-3215	102	212	,	,	PUNCT
cana-3215	102	213	1780	1780	NUM
cana-3215	102	214	,	,	PUNCT
cana-3215	102	215	890	890	NUM
cana-3215	102	216	,	,	PUNCT
cana-3215	102	217	445	445	NUM
cana-3215	102	218	,	,	PUNCT
cana-3215	102	219	1336	1336	NUM
cana-3215	102	220	,	,	PUNCT
cana-3215	102	221	668	668	NUM
cana-3215	102	222	,	,	PUNCT
cana-3215	102	223	334	334	NUM
cana-3215	102	224	,	,	PUNCT
cana-3215	102	225	167	167	NUM
cana-3215	102	226	,	,	PUNCT
cana-3215	102	227	502	502	NUM
cana-3215	102	228	,	,	PUNCT
cana-3215	102	229	251	251	NUM
cana-3215	102	230	,	,	PUNCT
cana-3215	102	231	754	754	NUM
cana-3215	102	232	,	,	PUNCT
cana-3215	102	233	377	377	NUM
cana-3215	102	234	,	,	PUNCT
cana-3215	102	235	1132	1132	NUM
cana-3215	102	236	,	,	PUNCT
cana-3215	102	237	566	566	NUM
cana-3215	102	238	,	,	PUNCT
cana-3215	102	239	283	283	NUM
cana-3215	102	240	,	,	PUNCT
cana-3215	102	241	850	850	NUM
cana-3215	102	242	,	,	PUNCT
cana-3215	102	243	425	425	NUM
cana-3215	102	244	,	,	PUNCT
cana-3215	102	245	1276	1276	NUM
cana-3215	102	246	,	,	PUNCT
cana-3215	102	247	638	638	NUM
cana-3215	102	248	,	,	PUNCT
cana-3215	102	249	319	319	NUM
cana-3215	102	250	,	,	PUNCT
cana-3215	102	251	958	958	NUM
cana-3215	102	252	,	,	PUNCT
cana-3215	102	253	479	479	NUM
cana-3215	102	254	,	,	PUNCT
cana-3215	102	255	1438	1438	NUM
cana-3215	102	256	,	,	PUNCT
cana-3215	102	257	719	719	NUM
cana-3215	102	258	,	,	PUNCT
cana-3215	102	259	2158	2158	NUM
cana-3215	102	260	,	,	PUNCT
cana-3215	102	261	1079	1079	NUM
cana-3215	102	262	,	,	PUNCT
cana-3215	102	263	3238	3238	NUM
cana-3215	102	264	,	,	PUNCT
cana-3215	102	265	1619	1619	NUM
cana-3215	102	266	,	,	PUNCT
cana-3215	102	267	4858	4858	NUM
cana-3215	102	268	,	,	PUNCT
cana-3215	102	269	2429	2429	NUM
cana-3215	102	270	,	,	PUNCT
cana-3215	102	271	7288	7288	NUM
cana-3215	102	272	,	,	PUNCT
cana-3215	102	273	3644	3644	NUM
cana-3215	102	274	,	,	PUNCT
cana-3215	102	275	1822	1822	NUM
cana-3215	102	276	,	,	PUNCT
cana-3215	102	277	911	911	NUM
cana-3215	102	278	,	,	PUNCT
cana-3215	102	279	2734	2734	NUM
cana-3215	102	280	,	,	PUNCT
cana-3215	102	281	1367	1367	NUM
cana-3215	102	282	,	,	PUNCT
cana-3215	102	283	4102	4102	NUM
cana-3215	102	284	,	,	PUNCT
cana-3215	102	285	2051	2051	NUM
cana-3215	102	286	,	,	PUNCT
cana-3215	102	287	6154	6154	NUM
cana-3215	102	288	,	,	PUNCT
cana-3215	102	289	3077	3077	NUM
cana-3215	102	290	,	,	PUNCT
cana-3215	102	291	9232	9232	NUM
cana-3215	102	292	,	,	PUNCT
cana-3215	102	293	4616	4616	NUM
cana-3215	102	294	,	,	PUNCT
cana-3215	102	295	2308	2308	NUM
cana-3215	102	296	,	,	PUNCT
cana-3215	102	297	1154	1154	NUM
cana-3215	102	298	,	,	PUNCT
cana-3215	102	299	577	577	NUM
cana-3215	102	300	,	,	PUNCT
cana-3215	102	301	1732	1732	NUM
cana-3215	102	302	,	,	PUNCT
cana-3215	102	303	866	866	NUM
cana-3215	102	304	,	,	PUNCT
cana-3215	102	305	433	433	NUM
cana-3215	102	306	,	,	PUNCT
cana-3215	102	307	1300	1300	NUM
cana-3215	102	308	,	,	PUNCT
cana-3215	102	309	650	650	NUM
cana-3215	102	310	,	,	PUNCT
cana-3215	102	311	325	325	NUM
cana-3215	102	312	,	,	PUNCT
cana-3215	102	313	976	976	NUM
cana-3215	102	314	,	,	PUNCT
cana-3215	102	315	488	488	NUM
cana-3215	102	316	,	,	PUNCT
cana-3215	102	317	244	244	NUM
cana-3215	102	318	,	,	PUNCT
cana-3215	102	319	122	122	NUM
cana-3215	102	320	,	,	PUNCT
cana-3215	102	321	61	61	NUM
cana-3215	102	322	,	,	PUNCT
cana-3215	102	323	184	184	NUM
cana-3215	102	324	,	,	PUNCT
cana-3215	102	325	92	92	NUM
cana-3215	102	326	,	,	PUNCT
cana-3215	102	327	46	46	NUM
cana-3215	102	328	,	,	PUNCT
cana-3215	102	329	23	23	NUM
cana-3215	102	330	,	,	PUNCT
cana-3215	102	331	70	70	NUM
cana-3215	102	332	,	,	PUNCT
cana-3215	102	333	35	35	NUM
cana-3215	102	334	,	,	PUNCT
cana-3215	102	335	106	106	NUM
cana-3215	102	336	,	,	PUNCT
cana-3215	102	337	53	53	NUM
cana-3215	102	338	,	,	PUNCT
cana-3215	102	339	160	160	NUM
cana-3215	102	340	,	,	PUNCT
cana-3215	102	341	80	80	NUM
cana-3215	102	342	,	,	PUNCT
cana-3215	102	343	40	40	NUM
cana-3215	102	344	,	,	PUNCT
cana-3215	102	345	20	20	NUM
cana-3215	102	346	,	,	PUNCT
cana-3215	102	347	10	10	NUM
cana-3215	102	348	,	,	PUNCT
cana-3215	102	349	5	5	NUM
cana-3215	102	350	,	,	PUNCT
cana-3215	102	351	16	16	NUM
cana-3215	102	352	,	,	PUNCT
cana-3215	102	353	8	8	NUM
cana-3215	102	354	,	,	PUNCT
cana-3215	102	355	4	4	NUM
cana-3215	102	356	,	,	PUNCT
cana-3215	102	357	2	2	NUM
cana-3215	102	358	,	,	PUNCT
cana-3215	102	359	1	1	NUM
cana-3215	102	360	,	,	PUNCT
cana-3215	102	361	4	4	NUM
cana-3215	102	362	,	,	PUNCT
cana-3215	102	363	2	2	NUM
cana-3215	102	364	,	,	PUNCT
cana-3215	102	365	1	1	NUM
cana-3215	102	366	n=100	n=100	NUM
cana-3215	102	367	collatz	collatz	NOUN
cana-3215	102	368	sequence	sequence	NOUN
cana-3215	102	369	:	:	PUNCT
cana-3215	102	370	100	100	NUM
cana-3215	102	371	,	,	PUNCT
cana-3215	102	372	50	50	NUM
cana-3215	102	373	,	,	PUNCT
cana-3215	102	374	25	25	NUM
cana-3215	102	375	,	,	PUNCT
cana-3215	102	376	76	76	NUM
cana-3215	102	377	,	,	PUNCT
cana-3215	102	378	38	38	NUM
cana-3215	102	379	,	,	PUNCT
cana-3215	102	380	19	19	NUM
cana-3215	102	381	,	,	PUNCT
cana-3215	102	382	58	58	NUM
cana-3215	102	383	,	,	PUNCT
cana-3215	102	384	29	29	NUM
cana-3215	102	385	,	,	PUNCT
cana-3215	102	386	88	88	NUM
cana-3215	102	387	,	,	PUNCT
cana-3215	102	388	44	44	NUM
cana-3215	102	389	,	,	PUNCT
cana-3215	102	390	22	22	NUM
cana-3215	102	391	,	,	PUNCT
cana-3215	102	392	11	11	NUM
cana-3215	102	393	,	,	PUNCT
cana-3215	102	394	34	34	NUM
cana-3215	102	395	,	,	PUNCT
cana-3215	102	396	17	17	NUM
cana-3215	102	397	,	,	PUNCT
cana-3215	102	398	52	52	NUM
cana-3215	102	399	,	,	PUNCT
cana-3215	102	400	26	26	NUM
cana-3215	102	401	,	,	PUNCT
cana-3215	102	402	13	13	NUM
cana-3215	102	403	,	,	PUNCT
cana-3215	102	404	40	40	NUM
cana-3215	102	405	,	,	PUNCT
cana-3215	102	406	20	20	NUM
cana-3215	102	407	,	,	PUNCT
cana-3215	102	408	10	10	NUM
cana-3215	102	409	,	,	PUNCT
cana-3215	102	410	5	5	NUM
cana-3215	102	411	,	,	PUNCT
cana-3215	102	412	16	16	NUM
cana-3215	102	413	,	,	PUNCT
cana-3215	102	414	8	8	NUM
cana-3215	102	415	,	,	PUNCT
cana-3215	102	416	4	4	NUM
cana-3215	102	417	,	,	PUNCT
cana-3215	102	418	2	2	NUM
cana-3215	102	419	,	,	PUNCT
cana-3215	102	420	1	1	NUM
cana-3215	102	421	,	,	PUNCT
cana-3215	102	422	4	4	NUM
cana-3215	102	423	,	,	PUNCT
cana-3215	102	424	2	2	NUM
cana-3215	102	425	,	,	PUNCT
cana-3215	102	426	1	1	NUM
cana-3215	102	427	n=155	n=155	NUM
cana-3215	102	428	collatz	collatz	NOUN
cana-3215	102	429	sequence	sequence	NOUN
cana-3215	102	430	:	:	PUNCT
cana-3215	102	431	155	155	NUM
cana-3215	102	432	,	,	PUNCT
cana-3215	102	433	466	466	NUM
cana-3215	102	434	,	,	PUNCT
cana-3215	102	435	233	233	NUM
cana-3215	102	436	,	,	PUNCT
cana-3215	102	437	700	700	NUM
cana-3215	102	438	,	,	PUNCT
cana-3215	102	439	350	350	NUM
cana-3215	102	440	,	,	PUNCT
cana-3215	102	441	175	175	NUM
cana-3215	102	442	,	,	PUNCT
cana-3215	102	443	526	526	NUM
cana-3215	102	444	,	,	PUNCT
cana-3215	102	445	263	263	NUM
cana-3215	102	446	,	,	PUNCT
cana-3215	102	447	790	790	NUM
cana-3215	102	448	,	,	PUNCT
cana-3215	102	449	395	395	NUM
cana-3215	102	450	,	,	PUNCT
cana-3215	102	451	1186	1186	NUM
cana-3215	102	452	,	,	PUNCT
cana-3215	102	453	593	593	NUM
cana-3215	102	454	,	,	PUNCT
cana-3215	102	455	1780	1780	NUM
cana-3215	102	456	,	,	PUNCT
cana-3215	102	457	890	890	NUM
cana-3215	102	458	,	,	PUNCT
cana-3215	102	459	445	445	NUM
cana-3215	102	460	,	,	PUNCT
cana-3215	102	461	1336	1336	NUM
cana-3215	102	462	,	,	PUNCT
cana-3215	102	463	668	668	NUM
cana-3215	102	464	,	,	PUNCT
cana-3215	102	465	334	334	NUM
cana-3215	102	466	,	,	PUNCT
cana-3215	102	467	167	167	NUM
cana-3215	102	468	,	,	PUNCT
cana-3215	102	469	502	502	NUM
cana-3215	102	470	,	,	PUNCT
cana-3215	102	471	251	251	NUM
cana-3215	102	472	,	,	PUNCT
cana-3215	102	473	754	754	NUM
cana-3215	102	474	,	,	PUNCT
cana-3215	102	475	377	377	NUM
cana-3215	102	476	,	,	PUNCT
cana-3215	102	477	1132	1132	NUM
cana-3215	102	478	,	,	PUNCT
cana-3215	102	479	566	566	NUM
cana-3215	102	480	,	,	PUNCT
cana-3215	102	481	283	283	NUM
cana-3215	102	482	,	,	PUNCT
cana-3215	102	483	850	850	NUM
cana-3215	102	484	,	,	PUNCT
cana-3215	102	485	425	425	NUM
cana-3215	102	486	,	,	PUNCT
cana-3215	102	487	1276	1276	NUM
cana-3215	102	488	,	,	PUNCT
cana-3215	102	489	638	638	NUM
cana-3215	102	490	,	,	PUNCT
cana-3215	102	491	319	319	NUM
cana-3215	102	492	,	,	PUNCT
cana-3215	102	493	958	958	NUM
cana-3215	102	494	,	,	PUNCT
cana-3215	102	495	479	479	NUM
cana-3215	102	496	,	,	PUNCT
cana-3215	102	497	communications	communication	NOUN
cana-3215	102	498	on	on	ADP
cana-3215	102	499	applied	apply	VERB
cana-3215	102	500	nonlinear	nonlinear	ADJ
cana-3215	102	501	analysis	analysis	NOUN
cana-3215	102	502	issn	issn	NOUN
cana-3215	102	503	:	:	PUNCT
cana-3215	102	504	1074	1074	NUM
cana-3215	102	505	-	-	PUNCT
cana-3215	102	506	133x	133x	NUM
cana-3215	102	507	vol	vol	NOUN
cana-3215	102	508	32	32	NUM
cana-3215	102	509	no	no	NOUN
cana-3215	102	510	.	.	PUNCT
cana-3215	103	1	6s	6s	NUM
cana-3215	103	2	(	(	PUNCT
cana-3215	103	3	2025	2025	NUM
cana-3215	103	4	)	)	PUNCT
cana-3215	103	5	22	22	NUM
cana-3215	103	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3215	103	7	1438	1438	NUM
cana-3215	103	8	,	,	PUNCT
cana-3215	103	9	719	719	NUM
cana-3215	103	10	,	,	PUNCT
cana-3215	103	11	2158	2158	NUM
cana-3215	103	12	,	,	PUNCT
cana-3215	103	13	1079	1079	NUM
cana-3215	103	14	,	,	PUNCT
cana-3215	103	15	3238	3238	NUM
cana-3215	103	16	,	,	PUNCT
cana-3215	103	17	1619	1619	NUM
cana-3215	103	18	,	,	PUNCT
cana-3215	103	19	4858	4858	NUM
cana-3215	103	20	,	,	PUNCT
cana-3215	103	21	2429	2429	NUM
cana-3215	103	22	,	,	PUNCT
cana-3215	103	23	7288	7288	NUM
cana-3215	103	24	,	,	PUNCT
cana-3215	103	25	3644	3644	NUM
cana-3215	103	26	,	,	PUNCT
cana-3215	103	27	1822	1822	NUM
cana-3215	103	28	,	,	PUNCT
cana-3215	103	29	911	911	NUM
cana-3215	103	30	,	,	PUNCT
cana-3215	103	31	2734	2734	NUM
cana-3215	103	32	,	,	PUNCT
cana-3215	103	33	1367	1367	NUM
cana-3215	103	34	,	,	PUNCT
cana-3215	103	35	4102	4102	NUM
cana-3215	103	36	,	,	PUNCT
cana-3215	103	37	2051	2051	NUM
cana-3215	103	38	,	,	PUNCT
cana-3215	103	39	6154	6154	NUM
cana-3215	103	40	,	,	PUNCT
cana-3215	103	41	3077	3077	NUM
cana-3215	103	42	,	,	PUNCT
cana-3215	103	43	9232	9232	NUM
cana-3215	103	44	,	,	PUNCT
cana-3215	103	45	4616	4616	NUM
cana-3215	103	46	,	,	PUNCT
cana-3215	103	47	2308	2308	NUM
cana-3215	103	48	,	,	PUNCT
cana-3215	103	49	1154	1154	NUM
cana-3215	103	50	,	,	PUNCT
cana-3215	103	51	577	577	NUM
cana-3215	103	52	,	,	PUNCT
cana-3215	103	53	1732	1732	NUM
cana-3215	103	54	,	,	PUNCT
cana-3215	103	55	866	866	NUM
cana-3215	103	56	,	,	PUNCT
cana-3215	103	57	433	433	NUM
cana-3215	103	58	,	,	PUNCT
cana-3215	103	59	1300	1300	NUM
cana-3215	103	60	,	,	PUNCT
cana-3215	103	61	650	650	NUM
cana-3215	103	62	,	,	PUNCT
cana-3215	103	63	325	325	NUM
cana-3215	103	64	,	,	PUNCT
cana-3215	103	65	976	976	NUM
cana-3215	103	66	,	,	PUNCT
cana-3215	103	67	488	488	NUM
cana-3215	103	68	,	,	PUNCT
cana-3215	103	69	244	244	NUM
cana-3215	103	70	,	,	PUNCT
cana-3215	103	71	122	122	NUM
cana-3215	103	72	,	,	PUNCT
cana-3215	103	73	61	61	NUM
cana-3215	103	74	,	,	PUNCT
cana-3215	103	75	184	184	NUM
cana-3215	103	76	,	,	PUNCT
cana-3215	103	77	92	92	NUM
cana-3215	103	78	,	,	PUNCT
cana-3215	103	79	46	46	NUM
cana-3215	103	80	,	,	PUNCT
cana-3215	103	81	23	23	NUM
cana-3215	103	82	,	,	PUNCT
cana-3215	103	83	70	70	NUM
cana-3215	103	84	,	,	PUNCT
cana-3215	103	85	35	35	NUM
cana-3215	103	86	,	,	PUNCT
cana-3215	103	87	106	106	NUM
cana-3215	103	88	,	,	PUNCT
cana-3215	103	89	53	53	NUM
cana-3215	103	90	,	,	PUNCT
cana-3215	103	91	160	160	NUM
cana-3215	103	92	,	,	PUNCT
cana-3215	103	93	80	80	NUM
cana-3215	103	94	,	,	PUNCT
cana-3215	103	95	40	40	NUM
cana-3215	103	96	,	,	PUNCT
cana-3215	103	97	20	20	NUM
cana-3215	103	98	,	,	PUNCT
cana-3215	103	99	10	10	NUM
cana-3215	103	100	,	,	PUNCT
cana-3215	103	101	5	5	NUM
cana-3215	103	102	,	,	PUNCT
cana-3215	103	103	16	16	NUM
cana-3215	103	104	,	,	PUNCT
cana-3215	103	105	8	8	NUM
cana-3215	103	106	,	,	PUNCT
cana-3215	103	107	4	4	NUM
cana-3215	103	108	,	,	PUNCT
cana-3215	103	109	2	2	NUM
cana-3215	103	110	,	,	PUNCT
cana-3215	103	111	1	1	NUM
cana-3215	103	112	,	,	PUNCT
cana-3215	103	113	4	4	NUM
cana-3215	103	114	,	,	PUNCT
cana-3215	103	115	2	2	NUM
cana-3215	103	116	,	,	PUNCT
cana-3215	103	117	1	1	NUM
cana-3215	103	118	n=217	n=217	NOUN
cana-3215	103	119	collatz	collatz	NOUN
cana-3215	103	120	sequence	sequence	NOUN
cana-3215	103	121	:	:	PUNCT
cana-3215	103	122	217	217	NUM
cana-3215	103	123	,	,	PUNCT
cana-3215	103	124	652	652	NUM
cana-3215	103	125	,	,	PUNCT
cana-3215	103	126	326	326	NUM
cana-3215	103	127	,	,	PUNCT
cana-3215	103	128	163	163	NUM
cana-3215	103	129	,	,	PUNCT
cana-3215	103	130	490	490	NUM
cana-3215	103	131	,	,	PUNCT
cana-3215	103	132	245	245	NUM
cana-3215	103	133	,	,	PUNCT
cana-3215	103	134	736	736	NUM
cana-3215	103	135	,	,	PUNCT
cana-3215	103	136	368	368	NUM
cana-3215	103	137	,	,	PUNCT
cana-3215	103	138	184	184	NUM
cana-3215	103	139	,	,	PUNCT
cana-3215	103	140	92	92	NUM
cana-3215	103	141	,	,	PUNCT
cana-3215	103	142	46	46	NUM
cana-3215	103	143	,	,	PUNCT
cana-3215	103	144	23	23	NUM
cana-3215	103	145	,	,	PUNCT
cana-3215	103	146	70	70	NUM
cana-3215	103	147	,	,	PUNCT
cana-3215	103	148	35	35	NUM
cana-3215	103	149	,	,	PUNCT
cana-3215	103	150	106	106	NUM
cana-3215	103	151	,	,	PUNCT
cana-3215	103	152	53	53	NUM
cana-3215	103	153	,	,	PUNCT
cana-3215	103	154	160	160	NUM
cana-3215	103	155	,	,	PUNCT
cana-3215	103	156	80	80	NUM
cana-3215	103	157	,	,	PUNCT
cana-3215	103	158	40	40	NUM
cana-3215	103	159	,	,	PUNCT
cana-3215	103	160	20	20	NUM
cana-3215	103	161	,	,	PUNCT
cana-3215	103	162	10	10	NUM
cana-3215	103	163	,	,	PUNCT
cana-3215	103	164	5	5	NUM
cana-3215	103	165	,	,	PUNCT
cana-3215	103	166	16	16	NUM
cana-3215	103	167	,	,	PUNCT
cana-3215	103	168	8	8	NUM
cana-3215	103	169	,	,	PUNCT
cana-3215	103	170	4	4	NUM
cana-3215	103	171	,	,	PUNCT
cana-3215	103	172	2	2	NUM
cana-3215	103	173	,	,	PUNCT
cana-3215	103	174	1	1	NUM
cana-3215	103	175	,	,	PUNCT
cana-3215	103	176	4	4	NUM
cana-3215	103	177	,	,	PUNCT
cana-3215	103	178	2	2	NUM
cana-3215	103	179	,	,	PUNCT
cana-3215	103	180	1	1	NUM
cana-3215	103	181	n=590	n=590	NUM
cana-3215	103	182	collatz	collatz	NOUN
cana-3215	103	183	sequence	sequence	NOUN
cana-3215	103	184	:	:	PUNCT
cana-3215	103	185	590	590	NUM
cana-3215	103	186	,	,	PUNCT
cana-3215	103	187	295	295	NUM
cana-3215	103	188	,	,	PUNCT
cana-3215	103	189	886	886	NUM
cana-3215	103	190	,	,	PUNCT
cana-3215	103	191	443	443	NUM
cana-3215	103	192	,	,	PUNCT
cana-3215	103	193	1330	1330	NUM
cana-3215	103	194	,	,	PUNCT
cana-3215	103	195	665	665	NUM
cana-3215	103	196	,	,	PUNCT
cana-3215	103	197	1996	1996	NUM
cana-3215	103	198	,	,	PUNCT
cana-3215	103	199	998	998	NUM
cana-3215	103	200	,	,	PUNCT
cana-3215	103	201	499	499	NUM
cana-3215	103	202	,	,	PUNCT
cana-3215	103	203	1498	1498	NUM
cana-3215	103	204	,	,	PUNCT
cana-3215	103	205	749	749	NUM
cana-3215	103	206	,	,	PUNCT
cana-3215	103	207	2248	2248	NUM
cana-3215	103	208	,	,	PUNCT
cana-3215	103	209	1124	1124	NUM
cana-3215	103	210	,	,	PUNCT
cana-3215	103	211	562	562	NUM
cana-3215	103	212	,	,	PUNCT
cana-3215	103	213	281	281	NUM
cana-3215	103	214	,	,	PUNCT
cana-3215	103	215	844	844	NUM
cana-3215	103	216	,	,	PUNCT
cana-3215	103	217	422	422	NUM
cana-3215	103	218	,	,	PUNCT
cana-3215	103	219	211	211	NUM
cana-3215	103	220	,	,	PUNCT
cana-3215	103	221	634	634	NUM
cana-3215	103	222	,	,	PUNCT
cana-3215	103	223	317	317	NUM
cana-3215	103	224	,	,	PUNCT
cana-3215	103	225	952	952	NUM
cana-3215	103	226	,	,	PUNCT
cana-3215	103	227	476	476	NUM
cana-3215	103	228	,	,	PUNCT
cana-3215	103	229	238	238	NUM
cana-3215	103	230	,	,	PUNCT
cana-3215	103	231	119	119	NUM
cana-3215	103	232	,	,	PUNCT
cana-3215	103	233	358	358	NUM
cana-3215	103	234	,	,	PUNCT
cana-3215	103	235	179	179	NUM
cana-3215	103	236	,	,	PUNCT
cana-3215	103	237	538	538	NUM
cana-3215	103	238	,	,	PUNCT
cana-3215	103	239	269	269	NUM
cana-3215	103	240	,	,	PUNCT
cana-3215	103	241	808	808	NUM
cana-3215	103	242	,	,	PUNCT
cana-3215	103	243	404	404	NUM
cana-3215	103	244	,	,	PUNCT
cana-3215	103	245	202	202	NUM
cana-3215	103	246	,	,	PUNCT
cana-3215	103	247	101	101	NUM
cana-3215	103	248	,	,	PUNCT
cana-3215	103	249	304	304	NUM
cana-3215	103	250	,	,	PUNCT
cana-3215	103	251	152	152	NUM
cana-3215	103	252	,	,	PUNCT
cana-3215	103	253	76	76	NUM
cana-3215	103	254	,	,	PUNCT
cana-3215	103	255	38	38	NUM
cana-3215	103	256	,	,	PUNCT
cana-3215	103	257	19	19	NUM
cana-3215	103	258	,	,	PUNCT
cana-3215	103	259	58	58	NUM
cana-3215	103	260	,	,	PUNCT
cana-3215	103	261	29	29	NUM
cana-3215	103	262	,	,	PUNCT
cana-3215	103	263	88	88	NUM
cana-3215	103	264	,	,	PUNCT
cana-3215	103	265	44	44	NUM
cana-3215	103	266	,	,	PUNCT
cana-3215	103	267	22	22	NUM
cana-3215	103	268	,	,	PUNCT
cana-3215	103	269	11	11	NUM
cana-3215	103	270	,	,	PUNCT
cana-3215	103	271	34	34	NUM
cana-3215	103	272	,	,	PUNCT
cana-3215	103	273	17	17	NUM
cana-3215	103	274	,	,	PUNCT
cana-3215	103	275	52	52	NUM
cana-3215	103	276	,	,	PUNCT
cana-3215	103	277	26	26	NUM
cana-3215	103	278	,	,	PUNCT
cana-3215	103	279	13	13	NUM
cana-3215	103	280	,	,	PUNCT
cana-3215	103	281	40	40	NUM
cana-3215	103	282	,	,	PUNCT
cana-3215	103	283	20	20	NUM
cana-3215	103	284	,	,	PUNCT
cana-3215	103	285	10	10	NUM
cana-3215	103	286	,	,	PUNCT
cana-3215	103	287	5	5	NUM
cana-3215	103	288	,	,	PUNCT
cana-3215	103	289	16	16	NUM
cana-3215	103	290	,	,	PUNCT
cana-3215	103	291	8	8	NUM
cana-3215	103	292	,	,	PUNCT
cana-3215	103	293	4	4	NUM
cana-3215	103	294	,	,	PUNCT
cana-3215	103	295	2	2	NUM
cana-3215	103	296	,	,	PUNCT
cana-3215	103	297	1	1	NUM
cana-3215	103	298	,	,	PUNCT
cana-3215	103	299	4	4	NUM
cana-3215	103	300	,	,	PUNCT
cana-3215	103	301	2	2	NUM
cana-3215	103	302	,	,	PUNCT
cana-3215	103	303	1	1	NUM
cana-3215	103	304	n=2367	n=2367	PROPN
cana-3215	103	305	collatz	collatz	NOUN
cana-3215	103	306	sequence	sequence	NOUN
cana-3215	103	307	:	:	PUNCT
cana-3215	103	308	2367	2367	NUM
cana-3215	103	309	,	,	PUNCT
cana-3215	103	310	7102	7102	NUM
cana-3215	103	311	,	,	PUNCT
cana-3215	103	312	3551	3551	NUM
cana-3215	103	313	,	,	PUNCT
cana-3215	103	314	10654	10654	NUM
cana-3215	103	315	,	,	PUNCT
cana-3215	103	316	5327	5327	NUM
cana-3215	103	317	,	,	PUNCT
cana-3215	103	318	15982	15982	NUM
cana-3215	103	319	,	,	PUNCT
cana-3215	103	320	7991	7991	NUM
cana-3215	103	321	,	,	PUNCT
cana-3215	103	322	23974	23974	NUM
cana-3215	103	323	,	,	PUNCT
cana-3215	103	324	11987	11987	NUM
cana-3215	103	325	,	,	PUNCT
cana-3215	103	326	35962	35962	NUM
cana-3215	103	327	,	,	PUNCT
cana-3215	103	328	17981	17981	NUM
cana-3215	103	329	,	,	PUNCT
cana-3215	103	330	53944	53944	NUM
cana-3215	103	331	,	,	PUNCT
cana-3215	103	332	26972	26972	NUM
cana-3215	103	333	,	,	PUNCT
cana-3215	103	334	13486	13486	NUM
cana-3215	103	335	,	,	PUNCT
cana-3215	103	336	6743	6743	NUM
cana-3215	103	337	,	,	PUNCT
cana-3215	103	338	20230	20230	NUM
cana-3215	103	339	,	,	PUNCT
cana-3215	103	340	10115	10115	NUM
cana-3215	103	341	,	,	PUNCT
cana-3215	103	342	30346	30346	NUM
cana-3215	103	343	,	,	PUNCT
cana-3215	103	344	15173	15173	NUM
cana-3215	103	345	,	,	PUNCT
cana-3215	103	346	45520	45520	NUM
cana-3215	103	347	,	,	PUNCT
cana-3215	103	348	22760	22760	NUM
cana-3215	103	349	,	,	PUNCT
cana-3215	103	350	11380	11380	NUM
cana-3215	103	351	,	,	PUNCT
cana-3215	103	352	5690	5690	NUM
cana-3215	103	353	,	,	PUNCT
cana-3215	103	354	2845	2845	NUM
cana-3215	103	355	,	,	PUNCT
cana-3215	103	356	8536	8536	NUM
cana-3215	103	357	,	,	PUNCT
cana-3215	103	358	4268	4268	NUM
cana-3215	103	359	,	,	PUNCT
cana-3215	103	360	2134	2134	NUM
cana-3215	103	361	,	,	PUNCT
cana-3215	103	362	1067	1067	NUM
cana-3215	103	363	,	,	PUNCT
cana-3215	103	364	3202	3202	NUM
cana-3215	103	365	,	,	PUNCT
cana-3215	103	366	1601	1601	NUM
cana-3215	103	367	,	,	PUNCT
cana-3215	103	368	4804	4804	NUM
cana-3215	103	369	,	,	PUNCT
cana-3215	103	370	2402	2402	NUM
cana-3215	103	371	,	,	PUNCT
cana-3215	103	372	1201	1201	NUM
cana-3215	103	373	,	,	PUNCT
cana-3215	103	374	3604	3604	NUM
cana-3215	103	375	,	,	PUNCT
cana-3215	103	376	1802	1802	NUM
cana-3215	103	377	,	,	PUNCT
cana-3215	103	378	901	901	NUM
cana-3215	103	379	,	,	PUNCT
cana-3215	103	380	2704	2704	NUM
cana-3215	103	381	,	,	PUNCT
cana-3215	103	382	1352	1352	NUM
cana-3215	103	383	,	,	PUNCT
cana-3215	103	384	676	676	NUM
cana-3215	103	385	,	,	PUNCT
cana-3215	103	386	338	338	NUM
cana-3215	103	387	,	,	PUNCT
cana-3215	103	388	169	169	NUM
cana-3215	103	389	,	,	PUNCT
cana-3215	103	390	508	508	NUM
cana-3215	103	391	,	,	PUNCT
cana-3215	103	392	254	254	NUM
cana-3215	103	393	,	,	PUNCT
cana-3215	103	394	127	127	NUM
cana-3215	103	395	,	,	PUNCT
cana-3215	103	396	382	382	NUM
cana-3215	103	397	,	,	PUNCT
cana-3215	103	398	191	191	NUM
cana-3215	103	399	,	,	PUNCT
cana-3215	103	400	574	574	NUM
cana-3215	103	401	,	,	PUNCT
cana-3215	103	402	287	287	NUM
cana-3215	103	403	,	,	PUNCT
cana-3215	103	404	862	862	NUM
cana-3215	103	405	,	,	PUNCT
cana-3215	103	406	431	431	NUM
cana-3215	103	407	,	,	PUNCT
cana-3215	103	408	1294	1294	NUM
cana-3215	103	409	,	,	PUNCT
cana-3215	103	410	647	647	NUM
cana-3215	103	411	,	,	PUNCT
cana-3215	103	412	1942	1942	NUM
cana-3215	103	413	,	,	PUNCT
cana-3215	103	414	971	971	NUM
cana-3215	103	415	,	,	PUNCT
cana-3215	103	416	2914	2914	NUM
cana-3215	103	417	,	,	PUNCT
cana-3215	103	418	1457	1457	NUM
cana-3215	103	419	,	,	PUNCT
cana-3215	103	420	4372	4372	NUM
cana-3215	103	421	,	,	PUNCT
cana-3215	103	422	2186	2186	NUM
cana-3215	103	423	,	,	PUNCT
cana-3215	103	424	1093	1093	NUM
cana-3215	103	425	,	,	PUNCT
cana-3215	103	426	3280	3280	NUM
cana-3215	103	427	,	,	PUNCT
cana-3215	103	428	1640	1640	NUM
cana-3215	103	429	,	,	PUNCT
cana-3215	103	430	820	820	NUM
cana-3215	103	431	,	,	PUNCT
cana-3215	103	432	410	410	NUM
cana-3215	103	433	,	,	PUNCT
cana-3215	103	434	205	205	NUM
cana-3215	103	435	,	,	PUNCT
cana-3215	103	436	616	616	NUM
cana-3215	103	437	,	,	PUNCT
cana-3215	103	438	308	308	NUM
cana-3215	103	439	,	,	PUNCT
cana-3215	103	440	154	154	NUM
cana-3215	103	441	,	,	PUNCT
cana-3215	103	442	77	77	NUM
cana-3215	103	443	,	,	PUNCT
cana-3215	103	444	232	232	NUM
cana-3215	103	445	,	,	PUNCT
cana-3215	103	446	116	116	NUM
cana-3215	103	447	,	,	PUNCT
cana-3215	103	448	58	58	NUM
cana-3215	103	449	,	,	PUNCT
cana-3215	103	450	29	29	NUM
cana-3215	103	451	,	,	PUNCT
cana-3215	103	452	88	88	NUM
cana-3215	103	453	,	,	PUNCT
cana-3215	103	454	44	44	NUM
cana-3215	103	455	,	,	PUNCT
cana-3215	103	456	22	22	NUM
cana-3215	103	457	,	,	PUNCT
cana-3215	103	458	11	11	NUM
cana-3215	103	459	,	,	PUNCT
cana-3215	103	460	34	34	NUM
cana-3215	103	461	,	,	PUNCT
cana-3215	103	462	17	17	NUM
cana-3215	103	463	,	,	PUNCT
cana-3215	103	464	52	52	NUM
cana-3215	103	465	,	,	PUNCT
cana-3215	103	466	26	26	NUM
cana-3215	103	467	,	,	PUNCT
cana-3215	103	468	13	13	NUM
cana-3215	103	469	,	,	PUNCT
cana-3215	103	470	40	40	NUM
cana-3215	103	471	,	,	PUNCT
cana-3215	103	472	20	20	NUM
cana-3215	103	473	,	,	PUNCT
cana-3215	103	474	10	10	NUM
cana-3215	103	475	,	,	PUNCT
cana-3215	103	476	5	5	NUM
cana-3215	103	477	,	,	PUNCT
cana-3215	103	478	16	16	NUM
cana-3215	103	479	,	,	PUNCT
cana-3215	103	480	8	8	NUM
cana-3215	103	481	,	,	PUNCT
cana-3215	103	482	4	4	NUM
cana-3215	103	483	,	,	PUNCT
cana-3215	103	484	2	2	NUM
cana-3215	103	485	,	,	PUNCT
cana-3215	103	486	1	1	NUM
cana-3215	103	487	,	,	PUNCT
cana-3215	103	488	4	4	NUM
cana-3215	103	489	,	,	PUNCT
cana-3215	103	490	2	2	NUM
cana-3215	103	491	,	,	PUNCT
cana-3215	103	492	1	1	NUM
cana-3215	103	493	results	result	NOUN
cana-3215	103	494	and	and	CCONJ
cana-3215	103	495	discussions	discussion	NOUN
cana-3215	103	496	:	:	PUNCT
cana-3215	103	497	it	it	PRON
cana-3215	103	498	is	be	AUX
cana-3215	103	499	observed	observe	VERB
cana-3215	103	500	that	that	SCONJ
cana-3215	103	501	all	all	DET
cana-3215	103	502	the	the	DET
cana-3215	103	503	positive	positive	ADJ
cana-3215	103	504	numbers	number	NOUN
cana-3215	103	505	sequence	sequence	NOUN
cana-3215	103	506	eventually	eventually	ADV
cana-3215	103	507	reach	reach	VERB
cana-3215	103	508	the	the	DET
cana-3215	103	509	cycle	cycle	NOUN
cana-3215	103	510	4	4	NUM
cana-3215	103	511	,	,	PUNCT
cana-3215	103	512	2	2	NUM
cana-3215	103	513	,	,	PUNCT
cana-3215	103	514	1	1	NUM
cana-3215	103	515	ultimately	ultimately	ADV
cana-3215	103	516	.	.	PUNCT
cana-3215	104	1	it	it	PRON
cana-3215	104	2	is	be	AUX
cana-3215	104	3	tested	test	VERB
cana-3215	104	4	for	for	ADP
cana-3215	104	5	a	a	DET
cana-3215	104	6	very	very	ADV
cana-3215	104	7	high	high	ADJ
cana-3215	104	8	range	range	NOUN
cana-3215	104	9	of	of	ADP
cana-3215	104	10	numbers	number	NOUN
cana-3215	104	11	and	and	CCONJ
cana-3215	104	12	all	all	DET
cana-3215	104	13	those	those	DET
cana-3215	104	14	numbers	number	NOUN
cana-3215	104	15	sequence	sequence	NOUN
cana-3215	104	16	end	end	VERB
cana-3215	104	17	in	in	ADP
cana-3215	104	18	the	the	DET
cana-3215	104	19	cycle	cycle	NOUN
cana-3215	104	20	.	.	PUNCT
cana-3215	105	1	anantagraphs	anantagraph	NOUN
cana-3215	105	2	of	of	ADP
cana-3215	105	3	random	random	ADJ
cana-3215	105	4	positive	positive	ADJ
cana-3215	105	5	numbers	number	NOUN
cana-3215	105	6	show	show	VERB
cana-3215	105	7	that	that	SCONJ
cana-3215	105	8	every	every	DET
cana-3215	105	9	tested	test	VERB
cana-3215	105	10	number	number	NOUN
cana-3215	105	11	enters	enter	VERB
cana-3215	105	12	the	the	DET
cana-3215	105	13	triangular	triangular	ADJ
cana-3215	105	14	head	head	NOUN
cana-3215	105	15	of	of	ADP
cana-3215	105	16	their	their	PRON
cana-3215	105	17	ananta	ananta	NOUN
cana-3215	105	18	-	-	PUNCT
cana-3215	105	19	graph	graph	NOUN
cana-3215	105	20	representation	representation	NOUN
cana-3215	105	21	.	.	PUNCT
cana-3215	106	1	this	this	PRON
cana-3215	106	2	provides	provide	VERB
cana-3215	106	3	the	the	DET
cana-3215	106	4	graphical	graphical	ADJ
cana-3215	106	5	proof	proof	NOUN
cana-3215	106	6	of	of	ADP
cana-3215	106	7	the	the	DET
cana-3215	106	8	collatz	collatz	NOUN
cana-3215	106	9	conjecture	conjecture	NOUN
cana-3215	106	10	.	.	PUNCT
cana-3215	107	1	communications	communication	NOUN
cana-3215	107	2	on	on	ADP
cana-3215	107	3	applied	apply	VERB
cana-3215	107	4	nonlinear	nonlinear	ADJ
cana-3215	107	5	analysis	analysis	NOUN
cana-3215	107	6	issn	issn	NOUN
cana-3215	107	7	:	:	PUNCT
cana-3215	107	8	1074	1074	NUM
cana-3215	107	9	-	-	PUNCT
cana-3215	107	10	133x	133x	NUM
cana-3215	107	11	vol	vol	NOUN
cana-3215	107	12	32	32	NUM
cana-3215	107	13	no	no	NOUN
cana-3215	107	14	.	.	PUNCT
cana-3215	108	1	6s	6s	NUM
cana-3215	108	2	(	(	PUNCT
cana-3215	108	3	2025	2025	NUM
cana-3215	108	4	)	)	PUNCT
cana-3215	108	5	23	23	NUM
cana-3215	108	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3215	108	7	for	for	ADP
cana-3215	108	8	negative	negative	ADJ
cana-3215	108	9	numbers	number	NOUN
cana-3215	108	10	,	,	PUNCT
cana-3215	108	11	the	the	DET
cana-3215	108	12	ananta	ananta	NOUN
cana-3215	108	13	-	-	PUNCT
cana-3215	108	14	graph	graph	NOUN
cana-3215	108	15	can	can	AUX
cana-3215	108	16	be	be	AUX
cana-3215	108	17	plotted	plot	VERB
cana-3215	108	18	by	by	ADP
cana-3215	108	19	converting	convert	VERB
cana-3215	108	20	them	they	PRON
cana-3215	108	21	to	to	ADP
cana-3215	108	22	positive	positive	ADJ
cana-3215	108	23	numbers	number	NOUN
cana-3215	108	24	using	use	VERB
cana-3215	108	25	2	2	NUM
cana-3215	108	26	’s	’s	PART
cana-3215	108	27	complement	complement	NOUN
cana-3215	108	28	as	as	SCONJ
cana-3215	108	29	mentioned	mention	VERB
cana-3215	108	30	in	in	ADP
cana-3215	108	31	the	the	DET
cana-3215	108	32	pseudocode	pseudocode	NOUN
cana-3215	108	33	of	of	ADP
cana-3215	108	34	the	the	DET
cana-3215	108	35	python	python	PROPN
cana-3215	108	36	program	program	NOUN
cana-3215	108	37	.	.	PUNCT
cana-3215	109	1	the	the	DET
cana-3215	109	2	2	2	NUM
cana-3215	109	3	’s	’s	PART
cana-3215	109	4	complement	complement	NOUN
cana-3215	109	5	of	of	ADP
cana-3215	109	6	a	a	DET
cana-3215	109	7	negative	negative	ADJ
cana-3215	109	8	number	number	NOUN
cana-3215	109	9	is	be	AUX
cana-3215	109	10	a	a	DET
cana-3215	109	11	method	method	NOUN
cana-3215	109	12	used	use	VERB
cana-3215	109	13	in	in	ADP
cana-3215	109	14	computer	computer	NOUN
cana-3215	109	15	systems	system	NOUN
cana-3215	109	16	to	to	PART
cana-3215	109	17	represent	represent	VERB
cana-3215	109	18	signed	sign	VERB
cana-3215	109	19	integers	integer	NOUN
cana-3215	109	20	in	in	ADP
cana-3215	109	21	binary	binary	NOUN
cana-3215	109	22	.	.	PUNCT
cana-3215	110	1	it	it	PRON
cana-3215	110	2	is	be	AUX
cana-3215	110	3	done	do	VERB
cana-3215	110	4	by	by	ADP
cana-3215	110	5	representing	represent	VERB
cana-3215	110	6	a	a	DET
cana-3215	110	7	absolute	absolute	ADJ
cana-3215	110	8	value	value	NOUN
cana-3215	110	9	in	in	ADP
cana-3215	110	10	binary	binary	NOUN
cana-3215	110	11	,	,	PUNCT
cana-3215	110	12	inverting	invert	VERB
cana-3215	110	13	the	the	DET
cana-3215	110	14	each	each	DET
cana-3215	110	15	digit	digit	NOUN
cana-3215	110	16	(	(	PUNCT
cana-3215	110	17	1	1	NUM
cana-3215	110	18	’s	’s	PART
cana-3215	110	19	complement	complement	NOUN
cana-3215	110	20	)	)	PUNCT
cana-3215	110	21	and	and	CCONJ
cana-3215	110	22	increment	increment	VERB
cana-3215	110	23	it	it	PRON
cana-3215	110	24	by	by	ADP
cana-3215	110	25	1	1	NUM
cana-3215	110	26	.	.	X
cana-3215	111	1	note	note	VERB
cana-3215	111	2	that	that	SCONJ
cana-3215	111	3	,	,	PUNCT
cana-3215	111	4	in	in	ADP
cana-3215	111	5	this	this	DET
cana-3215	111	6	paper	paper	NOUN
cana-3215	111	7	,	,	PUNCT
cana-3215	111	8	we	we	PRON
cana-3215	111	9	have	have	AUX
cana-3215	111	10	considered	consider	VERB
cana-3215	111	11	8	8	NUM
cana-3215	111	12	-	-	PUNCT
cana-3215	111	13	bit	bit	NOUN
cana-3215	111	14	length	length	NOUN
cana-3215	111	15	.	.	PUNCT
cana-3215	112	1	below	below	ADV
cana-3215	112	2	are	be	AUX
cana-3215	112	3	some	some	DET
cana-3215	112	4	negative	negative	ADJ
cana-3215	112	5	numbers	number	NOUN
cana-3215	112	6	and	and	CCONJ
cana-3215	112	7	their	their	PRON
cana-3215	112	8	positive	positive	ADJ
cana-3215	112	9	counterparts	counterpart	NOUN
cana-3215	112	10	using	use	VERB
cana-3215	112	11	2	2	NUM
cana-3215	112	12	’s	’s	PART
cana-3215	112	13	complement	complement	NOUN
cana-3215	112	14	.	.	PUNCT
cana-3215	113	1	negative	negative	ADJ
cana-3215	113	2	number	number	NOUN
cana-3215	113	3	positive	positive	ADJ
cana-3215	113	4	number	number	NOUN
cana-3215	113	5	using	use	VERB
cana-3215	113	6	2	2	NUM
cana-3215	113	7	’s	’s	PART
cana-3215	113	8	complement	complement	NOUN
cana-3215	113	9	-3	-3	PUNCT
cana-3215	113	10	253	253	NUM
cana-3215	113	11	-17	-17	SYM
cana-3215	113	12	239	239	NUM
cana-3215	113	13	-85	-85	PROPN
cana-3215	113	14	171	171	NUM
cana-3215	114	1	-101	-101	PROPN
cana-3215	114	2	155	155	NUM
cana-3215	114	3	-255	-255	NUM
cana-3215	114	4	1	1	NUM
cana-3215	114	5	the	the	DET
cana-3215	114	6	number	number	NOUN
cana-3215	114	7	of	of	ADP
cana-3215	114	8	iterations	iteration	NOUN
cana-3215	114	9	/	/	SYM
cana-3215	114	10	steps	step	NOUN
cana-3215	114	11	taken	take	VERB
cana-3215	114	12	by	by	ADP
cana-3215	114	13	the	the	DET
cana-3215	114	14	integers	integer	NOUN
cana-3215	114	15	are	be	AUX
cana-3215	114	16	different	different	ADJ
cana-3215	114	17	from	from	ADP
cana-3215	114	18	each	each	DET
cana-3215	114	19	other	other	ADJ
cana-3215	114	20	to	to	PART
cana-3215	114	21	reach	reach	VERB
cana-3215	114	22	1	1	NUM
cana-3215	114	23	.	.	PUNCT
cana-3215	115	1	integer	integer	NOUN
cana-3215	115	2	number	number	NOUN
cana-3215	115	3	of	of	ADP
cana-3215	115	4	steps	step	NOUN
cana-3215	115	5	to	to	PART
cana-3215	115	6	reach	reach	VERB
cana-3215	115	7	1	1	NUM
cana-3215	115	8	integer	integer	NOUN
cana-3215	115	9	number	number	NOUN
cana-3215	115	10	of	of	ADP
cana-3215	115	11	steps	step	NOUN
cana-3215	115	12	to	to	PART
cana-3215	115	13	reach	reach	VERB
cana-3215	115	14	1	1	NUM
cana-3215	115	15	1	1	NUM
cana-3215	115	16	1	1	NUM
cana-3215	115	17	21	21	NUM
cana-3215	115	18	8	8	NUM
cana-3215	115	19	2	2	NUM
cana-3215	115	20	2	2	NUM
cana-3215	115	21	22	22	NUM
cana-3215	115	22	16	16	NUM
cana-3215	115	23	3	3	NUM
cana-3215	115	24	8	8	NUM
cana-3215	115	25	23	23	NUM
cana-3215	115	26	16	16	NUM
cana-3215	115	27	4	4	NUM
cana-3215	115	28	3	3	NUM
cana-3215	115	29	24	24	NUM
cana-3215	115	30	11	11	NUM
cana-3215	115	31	5	5	NUM
cana-3215	115	32	6	6	NUM
cana-3215	115	33	25	25	NUM
cana-3215	115	34	24	24	NUM
cana-3215	115	35	6	6	NUM
cana-3215	115	36	9	9	NUM
cana-3215	115	37	26	26	NUM
cana-3215	115	38	11	11	NUM
cana-3215	115	39	7	7	NUM
cana-3215	115	40	17	17	NUM
cana-3215	115	41	27	27	NUM
cana-3215	115	42	112	112	NUM
cana-3215	115	43	8	8	NUM
cana-3215	115	44	4	4	NUM
cana-3215	115	45	28	28	NUM
cana-3215	115	46	19	19	NUM
cana-3215	115	47	9	9	NUM
cana-3215	115	48	20	20	NUM
cana-3215	115	49	29	29	NUM
cana-3215	115	50	19	19	NUM
cana-3215	115	51	10	10	NUM
cana-3215	115	52	7	7	NUM
cana-3215	115	53	30	30	NUM
cana-3215	115	54	19	19	NUM
cana-3215	115	55	11	11	NUM
cana-3215	115	56	15	15	NUM
cana-3215	115	57	31	31	NUM
cana-3215	115	58	107	107	NUM
cana-3215	115	59	12	12	NUM
cana-3215	115	60	10	10	NUM
cana-3215	115	61	32	32	NUM
cana-3215	115	62	6	6	NUM
cana-3215	115	63	13	13	NUM
cana-3215	115	64	10	10	NUM
cana-3215	115	65	33	33	NUM
cana-3215	115	66	27	27	NUM
cana-3215	115	67	14	14	NUM
cana-3215	115	68	18	18	NUM
cana-3215	115	69	34	34	NUM
cana-3215	115	70	14	14	NUM
cana-3215	115	71	15	15	NUM
cana-3215	115	72	18	18	NUM
cana-3215	115	73	35	35	NUM
cana-3215	115	74	14	14	NUM
cana-3215	115	75	16	16	NUM
cana-3215	115	76	5	5	NUM
cana-3215	115	77	36	36	NUM
cana-3215	115	78	22	22	NUM
cana-3215	115	79	17	17	NUM
cana-3215	115	80	13	13	NUM
cana-3215	115	81	37	37	NUM
cana-3215	115	82	22	22	NUM
cana-3215	115	83	18	18	NUM
cana-3215	115	84	21	21	NUM
cana-3215	115	85	38	38	NUM
cana-3215	115	86	22	22	NUM
cana-3215	115	87	19	19	NUM
cana-3215	115	88	21	21	NUM
cana-3215	115	89	39	39	NUM
cana-3215	115	90	35	35	NUM
cana-3215	115	91	20	20	NUM
cana-3215	115	92	8	8	NUM
cana-3215	115	93	40	40	NUM
cana-3215	115	94	9	9	NUM
cana-3215	115	95	communications	communication	NOUN
cana-3215	115	96	on	on	ADP
cana-3215	115	97	applied	apply	VERB
cana-3215	115	98	nonlinear	nonlinear	ADJ
cana-3215	115	99	analysis	analysis	NOUN
cana-3215	115	100	issn	issn	NOUN
cana-3215	115	101	:	:	PUNCT
cana-3215	115	102	1074	1074	NUM
cana-3215	115	103	-	-	PUNCT
cana-3215	115	104	133x	133x	NUM
cana-3215	115	105	vol	vol	NOUN
cana-3215	115	106	32	32	NUM
cana-3215	115	107	no	no	NOUN
cana-3215	115	108	.	.	PUNCT
cana-3215	116	1	6s	6s	NUM
cana-3215	116	2	(	(	PUNCT
cana-3215	116	3	2025	2025	NUM
cana-3215	116	4	)	)	PUNCT
cana-3215	116	5	24	24	NUM
cana-3215	116	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3215	116	7	note	note	VERB
cana-3215	116	8	that	that	SCONJ
cana-3215	116	9	for	for	ADP
cana-3215	116	10	reference	reference	NOUN
cana-3215	116	11	,	,	PUNCT
cana-3215	116	12	we	we	PRON
cana-3215	116	13	have	have	AUX
cana-3215	116	14	taken	take	VERB
cana-3215	116	15	the	the	DET
cana-3215	116	16	numbers	number	NOUN
cana-3215	116	17	between	between	ADP
cana-3215	116	18	1	1	NUM
cana-3215	116	19	and	and	CCONJ
cana-3215	116	20	40	40	NUM
cana-3215	116	21	.	.	PUNCT
cana-3215	117	1	the	the	DET
cana-3215	117	2	above	above	ADJ
cana-3215	117	3	table	table	NOUN
cana-3215	117	4	contains	contain	VERB
cana-3215	117	5	the	the	DET
cana-3215	117	6	number	number	NOUN
cana-3215	117	7	and	and	CCONJ
cana-3215	117	8	its	its	PRON
cana-3215	117	9	iteration	iteration	NOUN
cana-3215	117	10	count	count	NOUN
cana-3215	117	11	to	to	PART
cana-3215	117	12	reach	reach	VERB
cana-3215	117	13	1	1	NUM
cana-3215	117	14	when	when	SCONJ
cana-3215	117	15	subjected	subject	VERB
cana-3215	117	16	to	to	ADP
cana-3215	117	17	collatz	collatz	PROPN
cana-3215	117	18	conjecture	conjecture	NOUN
cana-3215	117	19	.	.	PUNCT
cana-3215	118	1	based	base	VERB
cana-3215	118	2	on	on	ADP
cana-3215	118	3	this	this	DET
cana-3215	118	4	data	data	NOUN
cana-3215	118	5	,	,	PUNCT
cana-3215	118	6	following	follow	VERB
cana-3215	118	7	observations	observation	NOUN
cana-3215	118	8	are	be	AUX
cana-3215	118	9	made	make	VERB
cana-3215	118	10	:	:	PUNCT
cana-3215	118	11	1	1	X
cana-3215	118	12	.	.	X
cana-3215	118	13	even	even	ADV
cana-3215	118	14	-	-	PUNCT
cana-3215	118	15	odd	odd	ADJ
cana-3215	118	16	rule	rule	NOUN
cana-3215	118	17	dynamics	dynamic	NOUN
cana-3215	118	18	:	:	PUNCT
cana-3215	118	19	for	for	ADP
cana-3215	118	20	even	even	ADV
cana-3215	118	21	numbers	number	NOUN
cana-3215	118	22	,	,	PUNCT
cana-3215	118	23	the	the	DET
cana-3215	118	24	sequence	sequence	NOUN
cana-3215	118	25	halves	halve	VERB
cana-3215	118	26	the	the	DET
cana-3215	118	27	number	number	NOUN
cana-3215	118	28	to	to	ADP
cana-3215	118	29	a	a	DET
cana-3215	118	30	faster	fast	ADJ
cana-3215	118	31	reduction	reduction	NOUN
cana-3215	118	32	.	.	PUNCT
cana-3215	119	1	for	for	ADP
cana-3215	119	2	odd	odd	ADJ
cana-3215	119	3	numbers	number	NOUN
cana-3215	119	4	,	,	PUNCT
cana-3215	119	5	the	the	DET
cana-3215	119	6	sequence	sequence	NOUN
cana-3215	119	7	increases	increase	VERB
cana-3215	119	8	the	the	DET
cana-3215	119	9	number	number	NOUN
cana-3215	119	10	,	,	PUNCT
cana-3215	119	11	often	often	ADV
cana-3215	119	12	causing	cause	VERB
cana-3215	119	13	a	a	DET
cana-3215	119	14	temporary	temporary	ADJ
cana-3215	119	15	rise	rise	NOUN
cana-3215	119	16	before	before	ADP
cana-3215	119	17	reducing	reduce	VERB
cana-3215	119	18	again	again	ADV
cana-3215	119	19	.	.	PUNCT
cana-3215	120	1	this	this	DET
cana-3215	120	2	variation	variation	NOUN
cana-3215	120	3	creates	create	VERB
cana-3215	120	4	unpredictable	unpredictable	ADJ
cana-3215	120	5	patterns	pattern	NOUN
cana-3215	120	6	.	.	PUNCT
cana-3215	121	1	2	2	X
cana-3215	121	2	.	.	NUM
cana-3215	121	3	step	step	NOUN
cana-3215	121	4	count	count	NOUN
cana-3215	121	5	variation	variation	NOUN
cana-3215	121	6	:	:	PUNCT
cana-3215	121	7	different	different	ADJ
cana-3215	121	8	numbers	number	NOUN
cana-3215	121	9	have	have	VERB
cana-3215	121	10	widely	widely	ADV
cana-3215	121	11	varying	vary	VERB
cana-3215	121	12	step	step	NOUN
cana-3215	121	13	counts	count	NOUN
cana-3215	121	14	.	.	PUNCT
cana-3215	122	1	for	for	ADP
cana-3215	122	2	example	example	NOUN
cana-3215	122	3	:	:	PUNCT
cana-3215	122	4	starting	start	VERB
cana-3215	122	5	at	at	ADP
cana-3215	122	6	6	6	NUM
cana-3215	122	7	takes	take	VERB
cana-3215	122	8	9	9	NUM
cana-3215	122	9	steps	step	NOUN
cana-3215	122	10	to	to	PART
cana-3215	122	11	reach	reach	VERB
cana-3215	122	12	1	1	NUM
cana-3215	122	13	whereas	whereas	SCONJ
cana-3215	122	14	larger	large	ADJ
cana-3215	122	15	numbers	number	NOUN
cana-3215	122	16	like	like	ADP
cana-3215	122	17	27	27	NUM
cana-3215	122	18	takes	take	VERB
cana-3215	122	19	112	112	NUM
cana-3215	122	20	steps	step	NOUN
cana-3215	122	21	.	.	PUNCT
cana-3215	123	1	strating	strate	VERB
cana-3215	123	2	at	at	ADP
cana-3215	123	3	9	9	NUM
cana-3215	123	4	takes	takes	AUX
cana-3215	123	5	20	20	NUM
cana-3215	123	6	steps	step	NOUN
cana-3215	123	7	to	to	PART
cana-3215	123	8	reach	reach	VERB
cana-3215	123	9	1	1	NUM
cana-3215	123	10	and	and	CCONJ
cana-3215	123	11	large	large	ADJ
cana-3215	123	12	numbers	number	NOUN
cana-3215	123	13	like	like	ADP
cana-3215	123	14	24	24	NUM
cana-3215	123	15	takes	take	VERB
cana-3215	123	16	11	11	NUM
cana-3215	123	17	steps	step	NOUN
cana-3215	123	18	.	.	PUNCT
cana-3215	124	1	there	there	PRON
cana-3215	124	2	is	be	VERB
cana-3215	124	3	no	no	DET
cana-3215	124	4	clear	clear	ADJ
cana-3215	124	5	pattern	pattern	NOUN
cana-3215	124	6	or	or	CCONJ
cana-3215	124	7	formula	formula	NOUN
cana-3215	124	8	that	that	PRON
cana-3215	124	9	can	can	AUX
cana-3215	124	10	directly	directly	ADV
cana-3215	124	11	predict	predict	VERB
cana-3215	124	12	the	the	DET
cana-3215	124	13	number	number	NOUN
cana-3215	124	14	of	of	ADP
cana-3215	124	15	steps	step	NOUN
cana-3215	124	16	for	for	ADP
cana-3215	124	17	any	any	DET
cana-3215	124	18	arbitrary	arbitrary	ADJ
cana-3215	124	19	number	number	NOUN
cana-3215	124	20	without	without	ADP
cana-3215	124	21	running	run	VERB
cana-3215	124	22	the	the	DET
cana-3215	124	23	sequence	sequence	NOUN
cana-3215	124	24	.	.	PUNCT
cana-3215	125	1	3	3	X
cana-3215	125	2	.	.	X
cana-3215	125	3	growth	growth	NOUN
cana-3215	125	4	and	and	CCONJ
cana-3215	125	5	collapse	collapse	NOUN
cana-3215	125	6	cycles	cycle	NOUN
cana-3215	125	7	:	:	PUNCT
cana-3215	125	8	during	during	ADP
cana-3215	125	9	the	the	DET
cana-3215	125	10	sequence	sequence	NOUN
cana-3215	125	11	,	,	PUNCT
cana-3215	125	12	odd	odd	ADJ
cana-3215	125	13	numbers	number	NOUN
cana-3215	125	14	tend	tend	VERB
cana-3215	125	15	to	to	PART
cana-3215	125	16	cause	cause	VERB
cana-3215	125	17	temporary	temporary	ADJ
cana-3215	125	18	spikes	spike	NOUN
cana-3215	125	19	in	in	ADP
cana-3215	125	20	value	value	NOUN
cana-3215	125	21	before	before	ADP
cana-3215	125	22	eventually	eventually	ADV
cana-3215	125	23	collapsing	collapse	VERB
cana-3215	125	24	when	when	SCONJ
cana-3215	125	25	the	the	DET
cana-3215	125	26	even	even	ADJ
cana-3215	125	27	-	-	PUNCT
cana-3215	125	28	number	number	NOUN
cana-3215	125	29	rule	rule	NOUN
cana-3215	125	30	reduces	reduce	VERB
cana-3215	125	31	them	they	PRON
cana-3215	125	32	.	.	PUNCT
cana-3215	126	1	this	this	PRON
cana-3215	126	2	creates	create	VERB
cana-3215	126	3	a	a	DET
cana-3215	126	4	sawtooth	sawtooth	NOUN
cana-3215	126	5	-	-	PUNCT
cana-3215	126	6	like	like	ADJ
cana-3215	126	7	pattern	pattern	NOUN
cana-3215	126	8	in	in	ADP
cana-3215	126	9	many	many	ADJ
cana-3215	126	10	sequences	sequence	NOUN
cana-3215	126	11	.	.	PUNCT
cana-3215	127	1	this	this	DET
cana-3215	127	2	fluctuation	fluctuation	NOUN
cana-3215	127	3	between	between	ADP
cana-3215	127	4	growth	growth	NOUN
cana-3215	127	5	and	and	CCONJ
cana-3215	127	6	collapse	collapse	NOUN
cana-3215	127	7	is	be	AUX
cana-3215	127	8	unpredictable	unpredictable	ADJ
cana-3215	127	9	,	,	PUNCT
cana-3215	127	10	yet	yet	CCONJ
cana-3215	127	11	eventually	eventually	ADV
cana-3215	127	12	every	every	DET
cana-3215	127	13	tested	test	VERB
cana-3215	127	14	number	number	NOUN
cana-3215	127	15	collapses	collapse	VERB
cana-3215	127	16	at	at	ADP
cana-3215	127	17	1	1	NUM
cana-3215	127	18	.	.	NOUN
cana-3215	127	19	4	4	NUM
cana-3215	127	20	.	.	X
cana-3215	128	1	distribution	distribution	NOUN
cana-3215	128	2	of	of	ADP
cana-3215	128	3	step	step	NOUN
cana-3215	128	4	counts	count	NOUN
cana-3215	128	5	:	:	PUNCT
cana-3215	128	6	many	many	ADJ
cana-3215	128	7	small	small	ADJ
cana-3215	128	8	numbers	number	NOUN
cana-3215	128	9	take	take	VERB
cana-3215	128	10	relatively	relatively	ADV
cana-3215	128	11	few	few	ADJ
cana-3215	128	12	steps	step	NOUN
cana-3215	128	13	to	to	PART
cana-3215	128	14	reach	reach	VERB
cana-3215	128	15	1	1	NUM
cana-3215	128	16	,	,	PUNCT
cana-3215	128	17	but	but	CCONJ
cana-3215	128	18	as	as	ADP
cana-3215	128	19	the	the	DET
cana-3215	128	20	starting	start	VERB
cana-3215	128	21	number	number	NOUN
cana-3215	128	22	increases	increase	NOUN
cana-3215	128	23	,	,	PUNCT
cana-3215	128	24	the	the	DET
cana-3215	128	25	number	number	NOUN
cana-3215	128	26	of	of	ADP
cana-3215	128	27	steps	step	NOUN
cana-3215	128	28	needed	need	VERB
cana-3215	128	29	to	to	PART
cana-3215	128	30	reach	reach	VERB
cana-3215	128	31	1	1	NUM
cana-3215	128	32	tends	tend	VERB
cana-3215	128	33	to	to	PART
cana-3215	128	34	grow	grow	VERB
cana-3215	128	35	unpredictably	unpredictably	ADV
cana-3215	128	36	.	.	PUNCT
cana-3215	129	1	however	however	ADV
cana-3215	129	2	,	,	PUNCT
cana-3215	129	3	some	some	DET
cana-3215	129	4	large	large	ADJ
cana-3215	129	5	numbers	number	NOUN
cana-3215	129	6	behave	behave	VERB
cana-3215	129	7	unexpectedly	unexpectedly	ADV
cana-3215	129	8	and	and	CCONJ
cana-3215	129	9	take	take	VERB
cana-3215	129	10	fewer	few	ADJ
cana-3215	129	11	steps	step	NOUN
cana-3215	129	12	than	than	ADP
cana-3215	129	13	nearby	nearby	ADJ
cana-3215	129	14	small	small	ADJ
cana-3215	129	15	numbers	number	NOUN
cana-3215	129	16	.	.	PUNCT
cana-3215	130	1	this	this	DET
cana-3215	130	2	irregularity	irregularity	NOUN
cana-3215	130	3	makes	make	VERB
cana-3215	130	4	predicting	predict	VERB
cana-3215	130	5	step	step	NOUN
cana-3215	130	6	count	count	NOUN
cana-3215	130	7	challenging	challenging	ADJ
cana-3215	130	8	.	.	PUNCT
cana-3215	131	1	the	the	DET
cana-3215	131	2	collatz	collatz	NOUN
cana-3215	131	3	sequence	sequence	NOUN
cana-3215	131	4	is	be	AUX
cana-3215	131	5	a	a	DET
cana-3215	131	6	remarkable	remarkable	ADJ
cana-3215	131	7	example	example	NOUN
cana-3215	131	8	of	of	ADP
cana-3215	131	9	how	how	SCONJ
cana-3215	131	10	basic	basic	ADJ
cana-3215	131	11	operations	operation	NOUN
cana-3215	131	12	can	can	AUX
cana-3215	131	13	create	create	VERB
cana-3215	131	14	complex	complex	ADJ
cana-3215	131	15	and	and	CCONJ
cana-3215	131	16	fascinating	fascinating	ADJ
cana-3215	131	17	outcomes	outcome	NOUN
cana-3215	131	18	,	,	PUNCT
cana-3215	131	19	with	with	ADP
cana-3215	131	20	the	the	DET
cana-3215	131	21	number	number	NOUN
cana-3215	131	22	of	of	ADP
cana-3215	131	23	steps	step	NOUN
cana-3215	131	24	being	be	AUX
cana-3215	131	25	an	an	DET
cana-3215	131	26	intriguing	intriguing	ADJ
cana-3215	131	27	feature	feature	NOUN
cana-3215	131	28	for	for	ADP
cana-3215	131	29	deeper	deep	ADJ
cana-3215	131	30	exploration	exploration	NOUN
cana-3215	131	31	.	.	PUNCT
cana-3215	132	1	conclusion	conclusion	NOUN
cana-3215	132	2	:	:	PUNCT
cana-3215	132	3	the	the	DET
cana-3215	132	4	collatz	collatz	NOUN
cana-3215	132	5	conjecture	conjecture	VERB
cana-3215	132	6	is	be	AUX
cana-3215	132	7	a	a	DET
cana-3215	132	8	profound	profound	ADJ
cana-3215	132	9	example	example	NOUN
cana-3215	132	10	of	of	ADP
cana-3215	132	11	how	how	SCONJ
cana-3215	132	12	a	a	DET
cana-3215	132	13	seemingly	seemingly	ADV
cana-3215	132	14	straight	straight	ADJ
cana-3215	132	15	forward	forward	ADV
cana-3215	132	16	mathematical	mathematical	ADJ
cana-3215	132	17	process	process	NOUN
cana-3215	132	18	can	can	AUX
cana-3215	132	19	hide	hide	VERB
cana-3215	132	20	deep	deep	ADJ
cana-3215	132	21	,	,	PUNCT
cana-3215	132	22	unresolved	unresolved	ADJ
cana-3215	132	23	mysteries	mystery	NOUN
cana-3215	132	24	.	.	PUNCT
cana-3215	133	1	the	the	DET
cana-3215	133	2	conjecture	conjecture	NOUN
cana-3215	133	3	’s	’s	PART
cana-3215	133	4	rules	rule	NOUN
cana-3215	133	5	are	be	AUX
cana-3215	133	6	simple	simple	ADJ
cana-3215	133	7	,	,	PUNCT
cana-3215	133	8	but	but	CCONJ
cana-3215	133	9	the	the	DET
cana-3215	133	10	behaviour	behaviour	NOUN
cana-3215	133	11	of	of	ADP
cana-3215	133	12	the	the	DET
cana-3215	133	13	sequence	sequence	NOUN
cana-3215	133	14	is	be	AUX
cana-3215	133	15	complex	complex	ADJ
cana-3215	133	16	and	and	CCONJ
cana-3215	133	17	unpredictable	unpredictable	ADJ
cana-3215	133	18	.	.	PUNCT
cana-3215	134	1	the	the	DET
cana-3215	134	2	sequence	sequence	NOUN
cana-3215	134	3	often	often	ADV
cana-3215	134	4	exhibits	exhibit	VERB
cana-3215	134	5	alternating	alternate	VERB
cana-3215	134	6	periods	period	NOUN
cana-3215	134	7	of	of	ADP
cana-3215	134	8	growth	growth	NOUN
cana-3215	134	9	and	and	CCONJ
cana-3215	134	10	rapid	rapid	ADJ
cana-3215	134	11	decline	decline	NOUN
cana-3215	134	12	,	,	PUNCT
cana-3215	134	13	especially	especially	ADV
cana-3215	134	14	for	for	ADP
cana-3215	134	15	odd	odd	ADJ
cana-3215	134	16	numbers	number	NOUN
cana-3215	134	17	that	that	PRON
cana-3215	134	18	temporarily	temporarily	ADV
cana-3215	134	19	increase	increase	VERB
cana-3215	134	20	before	before	ADP
cana-3215	134	21	eventually	eventually	ADV
cana-3215	134	22	collapsing	collapse	VERB
cana-3215	134	23	due	due	ADJ
cana-3215	134	24	to	to	ADP
cana-3215	134	25	repeated	repeat	VERB
cana-3215	134	26	division	division	NOUN
cana-3215	134	27	by	by	ADP
cana-3215	134	28	2	2	NUM
cana-3215	134	29	.	.	PUNCT
cana-3215	134	30	to	to	PART
cana-3215	134	31	study	study	VERB
cana-3215	134	32	these	these	DET
cana-3215	134	33	sequences	sequence	NOUN
cana-3215	134	34	,	,	PUNCT
cana-3215	134	35	we	we	PRON
cana-3215	134	36	have	have	AUX
cana-3215	134	37	introduced	introduce	VERB
cana-3215	134	38	ananta	ananta	NOUN
cana-3215	134	39	-	-	PUNCT
cana-3215	134	40	graphs	graph	NOUN
cana-3215	134	41	,	,	PUNCT
cana-3215	134	42	which	which	PRON
cana-3215	134	43	communications	communication	NOUN
cana-3215	134	44	on	on	ADP
cana-3215	134	45	applied	apply	VERB
cana-3215	134	46	nonlinear	nonlinear	ADJ
cana-3215	134	47	analysis	analysis	NOUN
cana-3215	134	48	issn	issn	NOUN
cana-3215	134	49	:	:	PUNCT
cana-3215	134	50	1074	1074	NUM
cana-3215	134	51	-	-	PUNCT
cana-3215	134	52	133x	133x	NUM
cana-3215	134	53	vol	vol	NOUN
cana-3215	134	54	32	32	NUM
cana-3215	134	55	no	no	NOUN
cana-3215	134	56	.	.	PUNCT
cana-3215	135	1	6s	6s	NUM
cana-3215	135	2	(	(	PUNCT
cana-3215	135	3	2025	2025	NUM
cana-3215	135	4	)	)	PUNCT
cana-3215	135	5	25	25	NUM
cana-3215	135	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3215	135	7	offer	offer	VERB
cana-3215	135	8	a	a	DET
cana-3215	135	9	compelling	compelling	ADJ
cana-3215	135	10	visualization	visualization	NOUN
cana-3215	135	11	of	of	ADP
cana-3215	135	12	the	the	DET
cana-3215	135	13	collatz	collatz	NOUN
cana-3215	135	14	conjecture	conjecture	NOUN
cana-3215	135	15	,	,	PUNCT
cana-3215	135	16	where	where	SCONJ
cana-3215	135	17	all	all	DET
cana-3215	135	18	the	the	DET
cana-3215	135	19	positive	positive	ADJ
cana-3215	135	20	integers	integer	NOUN
cana-3215	135	21	follow	follow	VERB
cana-3215	135	22	a	a	DET
cana-3215	135	23	trajectory	trajectory	NOUN
cana-3215	135	24	that	that	PRON
cana-3215	135	25	eventually	eventually	ADV
cana-3215	135	26	leads	lead	VERB
cana-3215	135	27	to	to	ADP
cana-3215	135	28	the	the	DET
cana-3215	135	29	triangular	triangular	NOUN
cana-3215	135	30	cycle	cycle	NOUN
cana-3215	135	31	of	of	ADP
cana-3215	135	32	4	4	NUM
cana-3215	135	33	,	,	PUNCT
cana-3215	135	34	2	2	NUM
cana-3215	135	35	,	,	PUNCT
cana-3215	135	36	1	1	NUM
cana-3215	135	37	.	.	PUNCT
cana-3215	136	1	the	the	DET
cana-3215	136	2	graph	graph	NOUN
cana-3215	136	3	’s	’s	PART
cana-3215	136	4	structure	structure	NOUN
cana-3215	136	5	,	,	PUNCT
cana-3215	136	6	with	with	ADP
cana-3215	136	7	its	its	PRON
cana-3215	136	8	triangular	triangular	NOUN
cana-3215	136	9	head	head	NOUN
cana-3215	136	10	and	and	CCONJ
cana-3215	136	11	infinitely	infinitely	ADV
cana-3215	136	12	branching	branch	VERB
cana-3215	136	13	tail	tail	NOUN
cana-3215	136	14	,	,	PUNCT
cana-3215	136	15	encapsulates	encapsulate	VERB
cana-3215	136	16	the	the	DET
cana-3215	136	17	core	core	NOUN
cana-3215	136	18	idea	idea	NOUN
cana-3215	136	19	that	that	SCONJ
cana-3215	136	20	no	no	ADV
cana-3215	136	21	matter	matter	ADV
cana-3215	136	22	how	how	SCONJ
cana-3215	136	23	large	large	ADJ
cana-3215	136	24	the	the	DET
cana-3215	136	25	number	number	NOUN
cana-3215	136	26	,	,	PUNCT
cana-3215	136	27	it	it	PRON
cana-3215	136	28	will	will	AUX
cana-3215	136	29	eventually	eventually	ADV
cana-3215	136	30	reach	reach	VERB
cana-3215	136	31	the	the	DET
cana-3215	136	32	same	same	ADJ
cana-3215	136	33	repeating	repeat	VERB
cana-3215	136	34	cycle	cycle	NOUN
cana-3215	136	35	.	.	PUNCT
cana-3215	137	1	this	this	DET
cana-3215	137	2	highlights	highlight	NOUN
cana-3215	137	3	both	both	CCONJ
cana-3215	137	4	the	the	DET
cana-3215	137	5	elegance	elegance	NOUN
cana-3215	137	6	and	and	CCONJ
cana-3215	137	7	mystery	mystery	NOUN
cana-3215	137	8	of	of	ADP
cana-3215	137	9	the	the	DET
cana-3215	137	10	collatz	collatz	NOUN
cana-3215	137	11	conjecture	conjecture	VERB
cana-3215	137	12	,	,	PUNCT
cana-3215	137	13	as	as	SCONJ
cana-3215	137	14	its	its	PRON
cana-3215	137	15	simple	simple	ADJ
cana-3215	137	16	rules	rule	NOUN
cana-3215	137	17	produce	produce	VERB
cana-3215	137	18	a	a	DET
cana-3215	137	19	complex	complex	ADJ
cana-3215	137	20	yet	yet	CCONJ
cana-3215	137	21	predictable	predictable	ADJ
cana-3215	137	22	pattern	pattern	NOUN
cana-3215	137	23	in	in	ADP
cana-3215	137	24	the	the	DET
cana-3215	137	25	graph	graph	NOUN
cana-3215	137	26	.	.	PUNCT
cana-3215	138	1	the	the	DET
cana-3215	138	2	negative	negative	ADJ
cana-3215	138	3	numbers	number	NOUN
cana-3215	138	4	are	be	AUX
cana-3215	138	5	also	also	ADV
cana-3215	138	6	exposed	expose	VERB
cana-3215	138	7	to	to	ADP
cana-3215	138	8	ananta	ananta	NOUN
cana-3215	138	9	-	-	PUNCT
cana-3215	138	10	graphs	graph	NOUN
cana-3215	138	11	by	by	ADP
cana-3215	138	12	converting	convert	VERB
cana-3215	138	13	them	they	PRON
cana-3215	138	14	to	to	ADP
cana-3215	138	15	positive	positive	ADJ
cana-3215	138	16	numbers	number	NOUN
cana-3215	138	17	using	use	VERB
cana-3215	138	18	2	2	NUM
cana-3215	138	19	’s	’s	PART
cana-3215	138	20	complement	complement	NOUN
cana-3215	138	21	.	.	PUNCT
cana-3215	139	1	ananta	ananta	NOUN
cana-3215	139	2	-	-	PUNCT
cana-3215	139	3	graphs	graph	NOUN
cana-3215	139	4	provide	provide	VERB
cana-3215	139	5	an	an	DET
cana-3215	139	6	intuitive	intuitive	ADJ
cana-3215	139	7	and	and	CCONJ
cana-3215	139	8	structured	structured	ADJ
cana-3215	139	9	way	way	NOUN
cana-3215	139	10	to	to	PART
cana-3215	139	11	explore	explore	VERB
cana-3215	139	12	the	the	DET
cana-3215	139	13	beaviour	beaviour	NOUN
cana-3215	139	14	of	of	ADP
cana-3215	139	15	sequences	sequence	NOUN
cana-3215	139	16	and	and	CCONJ
cana-3215	139	17	their	their	PRON
cana-3215	139	18	ultimate	ultimate	ADJ
cana-3215	139	19	convergence	convergence	NOUN
cana-3215	139	20	,	,	PUNCT
cana-3215	139	21	underscoring	underscore	VERB
cana-3215	139	22	the	the	DET
cana-3215	139	23	potential	potential	ADJ
cana-3215	139	24	infinite	infinite	ADJ
cana-3215	139	25	nature	nature	NOUN
cana-3215	139	26	of	of	ADP
cana-3215	139	27	number	number	NOUN
cana-3215	139	28	exploration	exploration	NOUN
cana-3215	139	29	.	.	PUNCT
cana-3215	140	1	future	future	ADJ
cana-3215	140	2	work	work	NOUN
cana-3215	140	3	:	:	PUNCT
cana-3215	140	4	we	we	PRON
cana-3215	140	5	would	would	AUX
cana-3215	140	6	be	be	AUX
cana-3215	140	7	exploring	explore	VERB
cana-3215	140	8	ananta	ananta	NOUN
cana-3215	140	9	-	-	PUNCT
cana-3215	140	10	graphs	graph	NOUN
cana-3215	140	11	to	to	ADP
cana-3215	140	12	a	a	DET
cana-3215	140	13	great	great	ADJ
cana-3215	140	14	extent	extent	NOUN
cana-3215	140	15	by	by	ADP
cana-3215	140	16	applying	apply	VERB
cana-3215	140	17	various	various	ADJ
cana-3215	140	18	graph	graph	NOUN
cana-3215	140	19	concepts	concept	NOUN
cana-3215	140	20	in	in	ADP
cana-3215	140	21	order	order	NOUN
cana-3215	140	22	to	to	PART
cana-3215	140	23	prove	prove	VERB
cana-3215	140	24	its	its	PRON
cana-3215	140	25	existence	existence	NOUN
cana-3215	140	26	and	and	CCONJ
cana-3215	140	27	uniqueness	uniqueness	NOUN
cana-3215	140	28	.	.	PUNCT
cana-3215	141	1	the	the	DET
cana-3215	141	2	collatz	collatz	NOUN
cana-3215	141	3	sequence	sequence	NOUN
cana-3215	141	4	will	will	AUX
cana-3215	141	5	be	be	AUX
cana-3215	141	6	represented	represent	VERB
cana-3215	141	7	in	in	ADP
cana-3215	141	8	various	various	ADJ
cana-3215	141	9	aspects	aspect	NOUN
cana-3215	141	10	of	of	ADP
cana-3215	141	11	graph	graph	NOUN
cana-3215	141	12	theory	theory	NOUN
cana-3215	141	13	to	to	PART
cana-3215	141	14	provide	provide	VERB
cana-3215	141	15	a	a	DET
cana-3215	141	16	valid	valid	ADJ
cana-3215	141	17	proof	proof	NOUN
cana-3215	141	18	using	use	VERB
cana-3215	141	19	the	the	DET
cana-3215	141	20	mathematical	mathematical	ADJ
cana-3215	141	21	tools	tool	NOUN
cana-3215	141	22	available	available	ADJ
cana-3215	141	23	.	.	PUNCT
cana-3215	142	1	reference	reference	NOUN
cana-3215	142	2	:	:	PUNCT
cana-3215	143	1	[	[	X
cana-3215	143	2	1	1	X
cana-3215	143	3	]	]	X
cana-3215	143	4	thijs	thijs	PROPN
cana-3215	143	5	laarhoven	laarhoven	PROPN
cana-3215	143	6	,	,	PUNCT
cana-3215	143	7	benne	benne	PROPN
cana-3215	143	8	de	de	PROPN
cana-3215	143	9	weger	weger	PROPN
cana-3215	143	10	,	,	PUNCT
cana-3215	143	11	the	the	DET
cana-3215	143	12	collatz	collatz	NOUN
cana-3215	143	13	conjecture	conjecture	NOUN
cana-3215	143	14	and	and	CCONJ
cana-3215	143	15	de	de	ADP
cana-3215	143	16	bruijn	bruijn	NOUN
cana-3215	143	17	graphs	graph	NOUN
cana-3215	143	18	,	,	PUNCT
cana-3215	143	19	indagationes	indagatione	NOUN
cana-3215	143	20	mathematicae	mathematicae	PROPN
cana-3215	143	21	,	,	PUNCT
cana-3215	143	22	volume	volume	NOUN
cana-3215	143	23	24	24	NUM
cana-3215	143	24	,	,	PUNCT
cana-3215	143	25	issue	issue	NOUN
cana-3215	143	26	4	4	NUM
cana-3215	143	27	,	,	PUNCT
cana-3215	143	28	2013	2013	NUM
cana-3215	143	29	,	,	PUNCT
cana-3215	143	30	pages	page	NOUN
cana-3215	143	31	971	971	NUM
cana-3215	143	32	-	-	SYM
cana-3215	143	33	983	983	NUM
cana-3215	143	34	.	.	PUNCT
cana-3215	144	1	[	[	X
cana-3215	144	2	2	2	NUM
cana-3215	144	3	]	]	PUNCT
cana-3215	144	4	machado	machado	PROPN
cana-3215	144	5	jat	jat	PROPN
cana-3215	144	6	,	,	PUNCT
cana-3215	144	7	galhano	galhano	VERB
cana-3215	144	8	a	a	PRON
cana-3215	144	9	,	,	PUNCT
cana-3215	144	10	cao	cao	PROPN
cana-3215	144	11	labora	labora	PROPN
cana-3215	144	12	d.	d.	PROPN
cana-3215	144	13	a	a	DET
cana-3215	144	14	clustering	cluster	VERB
cana-3215	144	15	perspective	perspective	NOUN
cana-3215	144	16	of	of	ADP
cana-3215	144	17	the	the	DET
cana-3215	144	18	collatz	collatz	NOUN
cana-3215	144	19	conjecture	conjecture	NOUN
cana-3215	144	20	.	.	PUNCT
cana-3215	145	1	mathematics	mathematic	NOUN
cana-3215	145	2	,	,	PUNCT
cana-3215	145	3	9(4	9(4	NOUN
cana-3215	145	4	)	)	PUNCT
cana-3215	145	5	,	,	PUNCT
cana-3215	145	6	2021	2021	NUM
cana-3215	145	7	,	,	PUNCT
cana-3215	145	8	314	314	NUM
cana-3215	145	9	.	.	PUNCT
cana-3215	146	1	[	[	X
cana-3215	146	2	3	3	NUM
cana-3215	146	3	]	]	PUNCT
cana-3215	146	4	bennassar	bennassar	ADJ
cana-3215	146	5	,	,	PUNCT
cana-3215	146	6	miguel	miguel	PROPN
cana-3215	146	7	c.	c.	PROPN
cana-3215	146	8	the	the	DET
cana-3215	146	9	collatz	collatz	PROPN
cana-3215	146	10	conjecture	conjecture	NOUN
cana-3215	146	11	interpreted	interpret	VERB
cana-3215	146	12	with	with	ADP
cana-3215	146	13	graph	graph	NOUN
cana-3215	146	14	theory	theory	NOUN
cana-3215	146	15	and	and	CCONJ
cana-3215	146	16	the	the	DET
cana-3215	146	17	properties	property	NOUN
cana-3215	146	18	of	of	ADP
cana-3215	146	19	the	the	DET
cana-3215	146	20	digital	digital	ADJ
cana-3215	146	21	root	root	NOUN
cana-3215	146	22	of	of	ADP
cana-3215	146	23	numbers	number	NOUN
cana-3215	146	24	:	:	PUNCT
cana-3215	146	25	an	an	DET
cana-3215	146	26	analytical	analytical	ADJ
cana-3215	146	27	approach	approach	NOUN
cana-3215	146	28	,	,	PUNCT
cana-3215	146	29	osf	osf	NOUN
cana-3215	146	30	preprints	preprint	NOUN
cana-3215	146	31	,	,	PUNCT
cana-3215	146	32	5	5	NUM
cana-3215	146	33	mar	mar	PROPN
cana-3215	146	34	.	.	PROPN
cana-3215	146	35	2023	2023	NUM
cana-3215	146	36	.	.	PUNCT
cana-3215	147	1	[	[	X
cana-3215	147	2	4	4	X
cana-3215	147	3	]	]	PUNCT
cana-3215	147	4	b.	b.	PROPN
cana-3215	147	5	u.	u.	PROPN
cana-3215	147	6	zaman	zaman	PROPN
cana-3215	147	7	,	,	PUNCT
cana-3215	147	8	exploring	explore	VERB
cana-3215	147	9	the	the	DET
cana-3215	147	10	collatz	collatz	NOUN
cana-3215	147	11	conjecture	conjecture	VERB
cana-3215	147	12	through	through	ADP
cana-3215	147	13	directed	direct	VERB
cana-3215	147	14	graphs	graph	NOUN
cana-3215	147	15	,	,	PUNCT
cana-3215	147	16	preprints	preprint	NOUN
cana-3215	147	17	,	,	PUNCT
cana-3215	147	18	(	(	PUNCT
cana-3215	147	19	2024	2024	NUM
cana-3215	147	20	)	)	PUNCT
cana-3215	147	21	,	,	PUNCT
cana-3215	147	22	2024020842	2024020842	NUM
cana-3215	147	23	.	.	PUNCT
cana-3215	148	1	[	[	X
cana-3215	148	2	5	5	NUM
cana-3215	148	3	]	]	X
cana-3215	148	4	wey	wey	PROPN
cana-3215	148	5	,	,	PUNCT
cana-3215	148	6	chin	chin	NOUN
cana-3215	148	7	-	-	PUNCT
cana-3215	148	8	long	long	ADV
cana-3215	148	9	,	,	PUNCT
cana-3215	148	10	"	"	PUNCT
cana-3215	148	11	proof	proof	NOUN
cana-3215	148	12	of	of	ADP
cana-3215	148	13	collatz	collatz	PROPN
cana-3215	148	14	conjecture	conjecture	NOUN
cana-3215	148	15	by	by	ADP
cana-3215	148	16	collatz	collatz	NOUN
cana-3215	148	17	graph	graph	NOUN
cana-3215	148	18	"	"	PUNCT
cana-3215	148	19	,	,	PUNCT
cana-3215	148	20	arxiv	arxiv	PROPN
cana-3215	148	21	preprint	preprint	NOUN
cana-3215	148	22	arxiv:2309.09991	arxiv:2309.09991	PROPN
cana-3215	148	23	,	,	PUNCT
cana-3215	148	24	(	(	PUNCT
cana-3215	148	25	2023	2023	NUM
cana-3215	148	26	)	)	PUNCT
cana-3215	148	27	.	.	PUNCT
cana-3215	149	1	[	[	X
cana-3215	149	2	6	6	NUM
cana-3215	149	3	]	]	X
cana-3215	149	4	zhou	zhou	PROPN
cana-3215	149	5	,	,	PUNCT
cana-3215	149	6	xinyi	xinyi	PROPN
cana-3215	149	7	,	,	PUNCT
cana-3215	149	8	proof	proof	NOUN
cana-3215	149	9	of	of	ADP
cana-3215	149	10	the	the	DET
cana-3215	149	11	collatz	collatz	NOUN
cana-3215	149	12	conjecture	conjecture	NOUN
cana-3215	149	13	using	use	VERB
cana-3215	149	14	logical	logical	ADJ
cana-3215	149	15	and	and	CCONJ
cana-3215	149	16	probabilistic	probabilistic	ADJ
cana-3215	149	17	approaches	approach	NOUN
cana-3215	149	18	,	,	PUNCT
cana-3215	149	19	osf	osf	NOUN
cana-3215	149	20	preprints	preprint	NOUN
cana-3215	149	21	,	,	PUNCT
cana-3215	149	22	13	13	NUM
cana-3215	149	23	may	may	PROPN
cana-3215	149	24	2024	2024	NUM
cana-3215	149	25	.	.	PUNCT
cana-3215	150	1	[	[	X
cana-3215	150	2	7	7	NUM
cana-3215	150	3	]	]	X
cana-3215	150	4	furuta	furuta	NOUN
cana-3215	150	5	.	.	PUNCT
cana-3215	151	1	m	m	PROPN
cana-3215	151	2	,	,	PUNCT
cana-3215	151	3	proof	proof	NOUN
cana-3215	151	4	of	of	ADP
cana-3215	151	5	collatz	collatz	NOUN
cana-3215	151	6	conjecture	conjecture	NOUN
cana-3215	151	7	using	use	VERB
cana-3215	151	8	division	division	NOUN
cana-3215	151	9	sequence	sequence	NOUN
cana-3215	151	10	,	,	PUNCT
cana-3215	151	11	advances	advance	NOUN
cana-3215	151	12	in	in	ADP
cana-3215	151	13	pure	pure	ADJ
cana-3215	151	14	mathematics	mathematic	NOUN
cana-3215	151	15	,	,	PUNCT
cana-3215	151	16	12	12	NUM
cana-3215	151	17	,	,	PUNCT
cana-3215	151	18	(	(	PUNCT
cana-3215	151	19	2022	2022	NUM
cana-3215	151	20	)	)	PUNCT
cana-3215	151	21	,	,	PUNCT
cana-3215	151	22	96	96	NUM
cana-3215	151	23	-	-	SYM
cana-3215	151	24	108	108	NUM
cana-3215	151	25	.	.	PUNCT