From Problem 435 I already made a fibonacci mod function, which I copied for this problem.
To find a(n) I use my Miller Primality Test, which is guaranteed to find primes, I simply try every number after n and see if it is a prime. I originally made the miller test for Problem 291 but didn't end up using, so glad it was useful!
But as it turned out once I got the correct answer, I tried using my Fermat Primality Test with 5 tests and it ended up being correct and faster...
Input an integer (yourinput)
∑b(n) mod 1234567891011 for 1 ≤ n ≤ yourinput