# Problem 492: Exploding sequence
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 x ≤ p ≤ x+y.
Examples: B(109, 103, 103) = 23674718882 B(109, 103, 1015) = 20731563854
Find B(109, 107, 1015).