A113517 Least k such that k^n-k+1 is prime, or 0 if there is no such k.

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

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: A343387 A083900 A369030 * A278399 A349197 A225416

Adjacent sequences: A113514 A113515 A113516 * A113518 A113519 A113520

Keyword

nonn

Author

T. D. Noe, Jan 12 2006

Status

approved