A225769 Least k>0 such that k^7+n is prime, or 0 if there is no such k.

0, 1, 1, 2, 1, 6, 1, 16, 9, 2, 1, 2, 1, 6, 5, 22, 1, 8, 1, 10, 3, 2, 1, 2, 17, 12, 3, 4, 1, 2, 1, 6, 5, 4, 3, 2, 1, 4, 5, 2, 1, 6, 1, 4, 23, 2, 1, 24, 5, 4, 3, 2, 1, 2, 5, 6, 3, 28, 1, 8, 1, 22, 39, 2, 3, 2, 1, 4, 5, 2, 1, 2, 1, 6, 9, 34, 7, 6, 1, 10, 3, 16, 1, 2, 23, 22, 3, 14, 1, 14, 23, 12, 9, 4, 3, 2, 1, 4, 9, 2, 1, 2, 1, 4, 5, 2, 1, 8, 1, 4, 3, 2, 1, 2, 23, 12, 5, 40, 31, 92, 7

Offset: 0

Author

M. F. Hasler, Jul 25 2013

Keywords

• nonn

Comments

See A225768 for motivation and references.

Crossrefs

See A085099, A225765--A225770 for the k^2, k^3, ..., k^8 analogs.

Programs

PARI

(a,b=5)->{#factor(x^b+a)~==1&for(n=1,9e9,ispseudoprime(n^b+a)&return(n));a==1 || print1("/*"factor(x^b+a)"*/")} \\ For illustrative purpose only. The polynomial is factored to avoid an infinite search loop when it is composite. But a factored polynomial can yield a prime when all factors but one equal 1. This happens for b=4, n=4, cf. A225766.