Reciprocal Sum of Palindromes

2018/03/01 by Phakhinkon Phunphayap, Phunphayap, Phakhinkon, Prapanpong Pongsriiam +1
Computer Science · Mathematics · #11A63 #11Y60 #40A25 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1803.00161

openalex publication_date 2018/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A positive integer n is said to be a palindrome in base b (or b-adic palindrome) if the representation of n = (a_k a_k-1 ⋯ a₀)_b in base b with a_k ≠ 0 has the symmetric property a_k-i = a_i for every i=0,1,2,… ,k. Let s_b be the reciprocal sum of all b-adic palindromes. It is not difficult to show that s_b converges. In this article, we obtain upper and lower bounds for s_b and the inequality s_b

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