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arXiv · 1803.00161

Reciprocal Sum of Palindromes

Phakhinkon Phunphayap·Prapanpong Pongsriiam
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Abstract

A positive integer $n$ is said to be a palindrome in base $b$ (or $b$-adic palindrome) if the representation of $n = (a_k a_{k-1} \cdots a_0)_b$ 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 numerical data are also given.

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Phakhinkon Phunphayap, Prapanpong Pongsriiam. 2018-03-01. Reciprocal Sum of Palindromes. https://arxiv.org/abs/1803.00161

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