[math-fun] Dual palindromes

Here's a question a friend and I have been looking at very casually, with only the partialest results: Given two bases B and C, what is the asymptotic fraction of positive integers that are palindromes when expressed to each base? Perhaps to make things simpler, assume that B and C are relatively prime. Or are each prime. In fact, just for definiteness, what is the expected number of integers between 1 and N that are palindromes both to base 2 and to base 3 ??? --Dan