projecteuler.net

Palindrome-containing strings

Published on Saturday, 25th October 2014, 07:00 pm; Solved by 198;
Difficulty rating: 70%

Problem 486

Let F5(n) be the number of strings s such that:

  • s consists only of '0's and '1's,
  • s has length at most n, and
  • s contains a palindromic substring of length at least 5.

For example, F5(4) = 0, F5(5) = 8, F5(6) = 42 and F5(11) = 3844.

Let D(L) be the number of integers n such that 5 ≤ n ≤ L and F5(n) is divisible by 87654321.

For example, D(107) = 0 and D(5·109) = 51.

Find D(1018).