• Corpus ID: 119319305

Reciprocal Sum of Palindromes

@article{Phunphayap2019ReciprocalSO,
title={Reciprocal Sum of Palindromes},
author={Phakhinkon Napp Phunphayap and Prapanpong Pongsriiam},
journal={J. Integer Seq.},
year={2019},
volume={22},
pages={19.8.6}
}
• Published 1 March 2018
• Mathematics, Computer Science
• J. Integer Seq.
A positive integer $n$ is said to be a palindrome in base $b$ (or $b$-adic palindrome) if the representation of $n = (a_k a_{k-1} \cdots a_0)_b$ in base $b$ with $a_k \neq 0$ has the symmetric property $a_{k-i} = a_i$ for every $i=0,1,2,\ldots ,k$. 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 $s_{b} <s_{b'}$ for $2\leq b<b'$. Its consequences and some…
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