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
Thailand

Abstract:

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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