Palindromes in Lucas Sequences

Abstract.

 In this paper, we show that if (u _n ) _n ≥ 0 is a Lucas sequence of integers whose roots are real quadratic units (like the Fibonacci sequence, for example), then for every integer b > 1 the density of the set of positive integers n such that |u _n | is a base b palindrome (i.e., the string of its base b digits reads the same from the left and from the right) is zero.