Journal of Integer Sequences, Vol. 22 (2019), Article 19.8.6

Reciprocal Sum of Palindromes

Phakhinkon Phunphayap and Prapanpong Pongsriiam
Department of Mathematics
Faculty of Science
Silpakorn University
Nakhon Pathom 73000


A positive integer n is a b-adic palindrome if the representation of n in base b reads the same backward as forward. Let sb be the reciprocal sum of all b-adic palindromes. In this article, we obtain upper and lower bounds, and an asymptotic formula for sb. We also show that the sequence (sb)b ≥ 2 is strictly increasing and log-concave.

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(Concerned with sequences A002113 A244162.)

Received May 27 2019; revised versions received October 7 2019; December 10 2019. Published in Journal of Integer Sequences, December 27 2019.

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