Quirky q's

Number Theory Level pending

The sequence q n q_n obeys the following equality:

q p k + 1 = p . q k 3 q p + 13 q_{pk+1}=p.q_k-3q_p+13 for every prime p and natural number k.

Find the sum of all possible q 2014 q_{2014}


The answer is 2017.

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