Sur la conjecture de Collatz

2016/07/08 by Vincent Fleckinger, Fleckinger, Vincent, Ibrahim Abdoulkarim +1
Mathematics · #Benford’s Law and Fraud Detection #math.NT

paper · pdf · doi:10.48550/arxiv.1607.02370

in French

arxiv created 2016/07/08 · arxiv updated 2016/07/11

Abstract

We give a generalization of Collatz conjecture or 3n+1 problem on 2-adic completion of Q. A isometric of Q₂ provides information on the average behavior of the firsts terms of the sequence according to the class of u₀ 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.

Related

• On the Collatz Problem
• Working with 2s and 3s
• On the Collatz general problem qn+1
• An Investigation of the Collatz Conjecture
• Proof of the Collatz Conjecture