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).
爆炸序列
定义序列 a1, a2, a3, … 如下：
- a1 = 1
- an+1 = 6an2 + 10an + 3 for n ≥ 1.
例如：
a3 = 2359
a6 = 269221280981320216750489044576319
a6 mod 1 000 000 007 = 203064689
a100 mod 1 000 000 007 = 456482974
对所有满足x ≤ p ≤ x+y的素数p，定义B(x,y,n)等于∑ (an mod p)。
例如：
B(109, 103, 103) = 23674718882
B(109, 103, 1015) = 20731563854
求B(109, 107, 1015)。