Sur la conjecture de Collatz

Abstract

We give a generalization of Collatz conjecture or 3n+1 problem on 2-adic completion of Q. A isometric of $Q_2$ provides information on the average behavior of the firsts terms of the sequence according to the class of $u_0$ modulo $2^m$. A generalisation from the pair (2,3) to the pair (p,q) seems possible under the assumption $q^{p-1}<p^p$.