Palindromes in linear recurrence sequences

Abstract

We prove that for any base \(b\ge 2\) and for any linear homogeneous recurrence sequence \(\{a_n\}_{n\ge 1}\) satisfying certain conditions, there exits a positive constant \(c>0\) such that \(\# \{n\le x:\ a_n \;\text{ is} \text{ palindromic} \text{ in} \text{ base}\; b\} \ll x^{1-c}\).