On Sloane's persistence problem

2013/07/04 by Edson de Faria, de Faria, Edson, Charles Tresser +1
Computer Science · Mathematics · Physics and Astronomy · #11K16 #37A15 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Primary 37E10 #Secondary 37A45 #Theoretical and Computational Physics #Topological and Geometric Data Analysis #math.DS #msc:11K16 #msc:37A15 #msc:37A45 #msc:37E10

paper · pdf · doi:10.48550/arxiv.1307.1188

5 figures

arxiv created 2013/07/04 · openalex publication_date 2013/07/04 · arxiv updated 2013/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the so-called persistence problem of Sloane, exploiting connections with the dynamics of circle maps and the ergodic theory of ℤ^d actions. We also formulate a conjecture concerning the asymptotic distribution of digits in long products of finitely many primes whose truth would, in particular, solve the persistence problem. The heuristics that we propose to complement our numerical studies can be thought in terms of a simple model in statistical mechanics.

Citations

• Endomorphisms and automorphisms of the shift dynamical system

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