Consecutive Integers and the Collatz Conjecture

Marcus Elia; Amanda Tucker

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arXiv · 1511.09141

Consecutive Integers and the Collatz Conjecture

Marcus Elia·Amanda Tucker

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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.

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Marcus Elia, Amanda Tucker. 2015-11-30. Consecutive Integers and the Collatz Conjecture. https://arxiv.org/abs/1511.09141

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