

A113517


Least k such that k^nk+1 is prime, or 0 if there is no such k.


2



2, 2, 3, 2, 3, 2, 0, 3, 4, 4, 4, 2, 0, 5, 18, 2, 12, 2, 0, 7, 3, 11, 13, 7, 0, 167, 15, 6, 63, 2, 0, 7, 6, 21, 49, 3, 0, 27, 30, 3, 22, 106, 0, 10, 30, 4, 294, 7, 0, 32, 19, 6, 7, 41, 0, 21, 4, 14, 34, 2, 0, 12, 13, 6, 147, 37, 0, 14, 139, 22, 46, 179, 0, 4, 75, 69, 15, 11, 0, 5, 211, 130
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OFFSET

2,1


COMMENTS

a(n) is 0 for n=8,14,20,... (n=2 mod 6) because, for those n, the polynomial x^nx+1 has the factor x^2x+1. Using a result of Selmer, it can be shown that x^nx+1 is irreducible for all other n. Does a(n) exist for all n>1?


LINKS

Table of n, a(n) for n=2..83.


MATHEMATICA

Table[f=FactorList[x^nx+1]; If[Length[f]>2, k=0, k=1; While[ !PrimeQ[k^nk+1], k++ ]]; k, {n, 2, 100}]


CROSSREFS

Cf. A113516 (smallest k such that n^kn+1 is prime).
Sequence in context: A156220 A261653 A083900 * A278399 A225416 A276862
Adjacent sequences: A113514 A113515 A113516 * A113518 A113519 A113520


KEYWORD

nonn


AUTHOR

T. D. Noe, Jan 12 2006


STATUS

approved



