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A113517 Least k such that k^n-k+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 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

a(n) is 0 for n=8,14,20,... (n=2 mod 6) because, for those n, the polynomial x^n-x+1 has the factor x^2-x+1. Using a result of Selmer, it can be shown that x^n-x+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^n-x+1]; If[Length[f]>2, k=0, k=1; While[ !PrimeQ[k^n-k+1], k++ ]]; k, {n, 2, 100}]

CROSSREFS

Cf. A113516 (smallest k such that n^k-n+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

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Last modified October 17 06:08 EDT 2019. Contains 328106 sequences. (Running on oeis4.)