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Exploding sequence

Published on Saturday, 6th December 2014, 01:00 pm; Solved by 271;
Difficulty rating: 60%

Problem 492

Define the sequence a1, a2, a3, ... as:

  • a1 = 1
  • an+1 = 6an2 + 10an + 3 for n ≥ 1.

Examples:
a3 = 2359
a6 = 269221280981320216750489044576319
a6 mod 1 000 000 007 = 203064689
a100 mod 1 000 000 007 = 456482974

Define B(x,y,n) as ∑ (an mod p) for every prime p such that xpx+y.

Examples:
B(109, 103, 103) = 23674718882
B(109, 103, 1015) = 20731563854

Find B(109, 107, 1015).