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A225770 Least k > 0 such that k^8 + n is prime, or 0 if there is no such k. 5

%I

%S 0,1,1,4,1,12,1,2,3,110,1,6,1,2,195,2,1,6,1,40,3,2,1,66,25,2,9,2,1,

%T 180,1,22,15,58,25,408,1,2,3,10,1,12,1,4,465,4,1,12,5,10,147,2,1,6,35,

%U 2,45,2,1,570,1,2,21,4,0,6,1,6,9,100,1

%N Least k > 0 such that k^8 + n is prime, or 0 if there is no such k.

%C See A225768 for motivation and references.

%e a(0) = 0 since k^8 is not prime for any k > 0.

%e a(4) = 1 since k^8 + 4 is prime for k = 1, although k^8 + 4 = (k^4 - 2k^2 + 2)(k^4 + 2k^2 + 2), but the first factor equals 1 for k = 1.

%e a(64) = 0 since k^8 + 64 = (k^4 - 4*k^2 + 8)(k^4 + 4k^2 + 8) which is composite for all integers k > 1.

%o (PARI) A225770(a,b=8)={#factor(x^b+a)~==1&for(n=1,9e9,ispseudoprime(n^b+a)&return(n));a==0 || a==64 || 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 n=4, cf. example.

%Y See A085099, A225765, ..., A225769 for the k^2, k^3, ..., k^7 analogs.

%K nonn

%O 0,4

%A _M. F. Hasler_, Jul 25 2013

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Last modified February 28 23:19 EST 2020. Contains 332353 sequences. (Running on oeis4.)