The number system in rational base $3/2$ and the $3x+1$ problem

Shalom Eliahou, Jean-Louis Verger-Gaugry

The representation of numbers in rational base $p/q$ was introduced in 2008 by Akiyama, Frougny & Sakarovitch, with a special focus on the case $p/q=3/2$. Unnoticed since then, nat…