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.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2017
- DOI:
- 10.48550/arXiv.1708.04615
- arXiv:
- arXiv:1708.04615
- Bibcode:
- 2017arXiv170804615P
- Keywords:
-
- Mathematics - General Mathematics;
- 11B83 (Primary);
- 11B37;
- 68Q99 (Secondary)
- E-Print:
- 14 pages, 4 figures and 6 tables Correction of typographic error in eq.(4.1), page 12