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Reciprocal Sum of Palindromes
A positive integer is said to be a palindrome in base (or -adic
palindrome) if the representation of in base
with has the symmetric property for every
. Let be the reciprocal sum of all -adic
palindromes. It is not difficult to show that converges. In this article,
we obtain upper and lower bounds for and the inequality
for . Its consequences and some numerical data are also given.Comment: updated and submitte