More Jabber about the Collatz Conjecture and a Closed Form for Detecting Cycles on Special Subsequences [Assertion: Collatz cycles]
Abstract
Professor Cadogan at the University of the West Indies identified special starting points that yield long subsequences where the normalization constant, k, is always one. I studied these special sequences and found an implicit mixed integer equation in closed form which if solved would produce seed values in cycling subsequences. Such cycles only occur among extremely large numbers, causing the equation to be difficult to solve numerically.
Keywords
Cite
@article{arxiv.1108.4056,
title = {More Jabber about the Collatz Conjecture and a Closed Form for Detecting Cycles on Special Subsequences [Assertion: Collatz cycles]},
author = {Thomas W. Lynch},
journal= {arXiv preprint arXiv:1108.4056},
year = {2011}
}
Comments
Write me if you would like a copy of the Mathematica program I used to search against the constraint. There are some variations for the closed form on other cases, write if you would like those. This work was done while I was visiting at the University of the West Indies this summer. I truly enjoyed meeting Dr. Cadogan and studying his Collatz conjecture proofs