## Palindromic sums

### Problem 125

Published on Friday, 4th August 2006, 06:00 pm; Solved by 8586; Difficulty rating: 25%The palindromic number 595 is interesting because it can be written as the sum of consecutive squares: 6^{2} + 7^{2} + 8^{2} + 9^{2} + 10^{2} + 11^{2} + 12^{2}.

There are exactly eleven palindromes below one-thousand that can be written as consecutive square sums, and the sum of these palindromes is 4164. Note that 1 = 0^{2} + 1^{2} has not been included as this problem is concerned with the squares of positive integers.

Find the sum of all the numbers less than 10^{8} that are both palindromic and can be written as the sum of consecutive squares.