ON "VERY PALINDROMIC" SEQUENCES

Title & Authors
ON "VERY PALINDROMIC" SEQUENCES
BASIC, BOJAN;

Abstract
We consider the problem of characterizing the palindromic sequences $\small{{\langle}c_{d-1},\;c_{d-2}\;,{\cdots},\;c_0\rangle}$, $\small{c_{d-1}{\neq}0}$, having the property that for any $\small{K{\in}\mathbb{N}}$ there exists a number that is a palindrome simultaneously in K different bases, with $\small{{\langle}c_{d-1},\;c_{d-2}\;,{\cdots},\;c_0\rangle}$ being its digit sequence in one of those bases. Since each number is trivially a palindrome in all bases greater than itself, we impose the restriction that only palindromes with at least two digits are taken into account. We further consider a related problem, where we count only palindromes with a fixed number of digits (that is, d). The first problem turns out not to be very hard; we show that all the palindromic sequences have the required property, even with the additional point that we can actually restrict the counted palindromes to have at least d digits. The second one is quite tougher; we show that all the palindromic sequences of length d
Keywords
palindrome;number base;heuristic;
Language
English
Cited by
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