2025/03/27 by Shashi Chourasiya, Daniel R. Johnston, Chourasiya, Shashi +1 · 1 citation
Computer Science · Mathematics · #11A63 (Primary) 11N37 #11Y35 (Secondary) #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2503.21136
openalex publication_date 2025/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove new results related to the digital reverse \overleftarrown of a positive integer n in a fixed base b. First we show that for b≥ 26000, there exists infinitely many primes p such that \overleftarrowp is square-free. Further, we show that for b≥ 2 there are infinitely many palindromes (with n=\overleftarrown) that are cube-free. We also give asymptotic expressions for the counting functions corresponding to these results. The main tools we use are recent bounds from the literature on reversed primes and palindromes in arithmetic progressions.