## Primonacci

### Problem 304

Published on Sunday, 3rd October 2010, 01:00 am; Solved by 1358; Difficulty rating: 35%
For any positive integer `n` the function next_prime(`n`) returns the smallest prime p

such that p>`n`.

The sequence a(`n`) is defined by:

a(1)=next_prime(10^{14}) and a(`n`)=next_prime(a(`n`-1)) for n>1.

The fibonacci sequence f(`n`) is defined by:
f(0)=0, f(1)=1 and f(`n`)=f(`n`-1)+f(`n`-2) for `n`>1.

The sequence b(`n`) is defined as f(a(`n`)).

Find ∑b(`n`) for 1≤`n`≤100 000.
Give your answer mod 1234567891011.