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arXiv · 1708.04615

Collatz Conjecture: Is It False?

Juan A. Perez
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Abstract

For a long time, Collatz Conjecture has been assumed to be true, although a formal proof has eluded all efforts to date. In this article, evidence is presented that suggests such an assumption is incorrect. By analysing the stopping times of various Collatz sequences, a pattern emerges that indicates the existence of non-empty sets of integers with stopping times greater than any given integer. This implies the existence of an infinite set of integers with non-finite stopping times, thus indicating the conjecture is false. Furthermore, a simple algorithm is constructed that finds integers with ever-greater stopping times. Such an algorithm does not halt, further supporting the conclusion that the conjecture is false.

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Juan A. Perez. 2017-08-15. Collatz Conjecture: Is It False?. https://arxiv.org/abs/1708.04615

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