Problem 304

Primonacci

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 n1.

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.

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These problems are part of
Project Euler
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