

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
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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



