  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 $q^{p-1}<p^p$.
