Counting relatively prime pairs of palindromes

For a given base $g\ge 2$, a positive integer is called a palindrome if its base $g$ expansion reads the same backwards as forwards. In this paper, we give an asymptotic formula for the number of relatively prime pairs of palindromes of a fixed odd length and of any base $g\ge 2$, which solves an open problem proposed by Banks and Shparlinski (2005).