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A225770 Least k > 0 such that k^8 + n is prime, or 0 if there is no such k. 5
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, 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, 2, 45, 2, 1, 570, 1, 2, 21, 4, 0, 6, 1, 6, 9, 100, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

See A225768 for motivation and references.

LINKS

Table of n, a(n) for n=0..70.

EXAMPLE

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

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.

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.

PROG

(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.

CROSSREFS

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

Sequence in context: A298362 A143952 A097877 * A019304 A072869 A064279

Adjacent sequences:  A225767 A225768 A225769 * A225771 A225772 A225773

KEYWORD

nonn

AUTHOR

M. F. Hasler, Jul 25 2013

STATUS

approved

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Last modified February 26 03:09 EST 2020. Contains 332272 sequences. (Running on oeis4.)