On the Behavior of Unbounded Collatz Sequences
Number Theory
2022-04-11 v2
Abstract
The aim of this paper is to show a peculiar behavior of a (hypothetical) Collatz sequence going to infinity. We study the associated Syracusa sequence (the odd elements of the former) and show that the limit set of a conveniently normalized sequence is the whole unit interval. In particular, for any positive integer there is a subsequence whose elements' expansions in base 3 begin (from the left) with the expansion of the given number.
Cite
@article{arxiv.2003.04615,
title = {On the Behavior of Unbounded Collatz Sequences},
author = {Jorge Salazar},
journal= {arXiv preprint arXiv:2003.04615},
year = {2022}
}