Consecutive Integers and the Collatz Conjecture

• Published in 2015
• Added on 2026-06-18

Pairs of consecutive integers have the same height in the Collatz problem with surprising frequency. Garner gave a conjectural family of conditions for exactly when this occurs. Our main result is an infinite family of counterexamples to Garner's conjecture.

Links

• https://arxiv.org/abs/1511.09141v1
• https://arxiv.org/pdf/1511.09141v1

Other information

BibTeX entry

@article{ConsecutiveIntegersandtheCollatzConjecture,
	key = {ConsecutiveIntegersandtheCollatzConjecture},
	type = {article},
	title = {Consecutive Integers and the Collatz Conjecture},
	author = {Marcus Elia and Amanda Tucker},
	abstract = {Pairs of consecutive integers have the same height in the Collatz problem with surprising frequency. Garner gave a conjectural family of conditions for exactly when this occurs. Our main result is an infinite family of counterexamples to Garner's conjecture.},
	comment = {},
	date_added = {2026-06-18},
	date_published = {2015-06-18},
	urls = {https://arxiv.org/abs/1511.09141v1,https://arxiv.org/pdf/1511.09141v1},
	collections = {drama,easily-explained,fun-maths-facts,integerology},
	url = {https://arxiv.org/abs/1511.09141v1 https://arxiv.org/pdf/1511.09141v1},
	year = 2015,
	urldate = {2026-06-18},
	archivePrefix = {arXiv},
	eprint = {1511.09141},
	primaryClass = {math.NT}
}