Palindromes in Lucas sequences (Q1404225)

Say that \(\{w_n\}\) is a Lucas sequence if \(w_{n+2}= rw_{n+1}+sw_n\) where \(s\neq 0\) and \(r^2+4s\neq 0\). An integer is called a palindrome to base \(b\) if the base \(b\) representation of the integer is left unchanged when the digits are reversed. Let \(P(x)\) denote the number of integers \(n\leq x\) such that \(w_n\) is a base \(b\) palindrome. Let \(\omega(b)\) denote the number of distinct prime factors of \(b\). The author's main result is that if the parameter \(s=\pm 1\), then \[ P(x)= O\Biggl( \frac{x}{(\log x)^c}\Biggr), \] where \(c= 1/2\omega(b)\).