Collatz Conjecture: Is It False?
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.
Cite
@article{arxiv.1708.04615,
title = {Collatz Conjecture: Is It False?},
author = {Juan A. Perez},
journal= {arXiv preprint arXiv:1708.04615},
year = {2017}
}
Comments
14 pages, 4 figures and 6 tables Correction of typographic error in eq.(4.1), page 12