Published on Sunday, 3rd October 2010, 01:00 am; Solved by 2055;
Difficulty rating: 40%

Problem 304

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(1014) 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.