The Collatz Problem generalized to 3x+k
Dynamical Systems
2021-01-21 v1
Abstract
The Collatz problem with is revisited. Positive and negative limit cycles are given up to k=9997 starting with . A simple relation between the probability distribution for the Syracuse iterates for various k (not divisible by 2 and 3) is obtained. From this it follows that the oscillation considered by Tao 2019 ( arXiv:1909.03562v2 ) does not depend on k. Thus this piece of the proof of his theorem 1.3 "Almost all Collatz orbits attain almost bounded values" holds for all k not divisible by 2 and 3.
Cite
@article{arxiv.2101.08060,
title = {The Collatz Problem generalized to 3x+k},
author = {Franz Wegner},
journal= {arXiv preprint arXiv:2101.08060},
year = {2021}
}
Comments
Main paper 13 pages; Supplement (278 pages) contains a list of limit cycles up to k=9997