On the nonexistence of cycles for the Collatz function
General Mathematics
2014-10-28 v8
Abstract
The Collatz function is defined as C(n) = n / 2 if n is even and C(n) = 3n + 1 if n is odd. The Collatz conjecture states that every sequence generated by the Collatz function ends with the cycle (4, 2, 1) after a finite number of iterations. In this paper it is shown that there exists no other cycle for the Collatz function.
Keywords
Cite
@article{arxiv.1208.2556,
title = {On the nonexistence of cycles for the Collatz function},
author = {Manfred Bork},
journal= {arXiv preprint arXiv:1208.2556},
year = {2014}
}
Comments
This paper has been withdrawn by the author because (k+1)n<k(n+2) is wrong