The number system in rational base $3/2$ and the $3x+1$ problem
Number Theory
2025-04-21 v1
Abstract
The representation of numbers in rational base was introduced in 2008 by Akiyama, Frougny & Sakarovitch, with a special focus on the case . Unnoticed since then, natural questions related to representations in that specific base turn out to intimately involve the Collatz function. Our purpose in this note is to expose these links and motivate further research into them.
Cite
@article{arxiv.2504.13716,
title = {The number system in rational base $3/2$ and the $3x+1$ problem},
author = {Shalom Eliahou and Jean-Louis Verger-Gaugry},
journal= {arXiv preprint arXiv:2504.13716},
year = {2025}
}
Comments
9 pages. To appear in Comptes Rendus. Math\'ematique. Acad\'emie des Sciences, Paris