A248079 Least number k such that k^n + k - 1 is prime, or 0 if no such k exists.

2, 2, 3, 2, 0, 4, 6, 2, 4, 3, 0, 17, 36, 3, 3, 2, 0, 6, 9, 43, 27, 9, 0, 3, 154, 3, 34, 54, 0, 24, 24, 6, 226, 23, 0, 3, 70, 36, 13, 51, 0, 4, 13, 9, 10, 68, 0, 18, 10, 45, 154, 85, 0, 23, 6, 10, 37, 8, 0, 30, 331, 9, 3, 40, 0, 11, 61, 8, 10, 35, 0, 61, 76, 54, 426, 9, 0, 84, 87, 13, 46

Offset: 1

Author

Derek Orr, Sep 30 2014

Keywords

• nonn

Comments

If n == 5 mod 6 (A016969), k^n + k - 1 is always divisible by k^2 - k + 1. Thus it will never be prime.

Crossrefs

Cf. A016969, A045546, A236475, A236759, A113517.

Programs

Mathematica

lnk[n_]:=Module[{k=2},While[CompositeQ[k^n+k-1],k++];k]; Table[If[Mod[n,6] == 5,0,lnk[n]],{n,90}] (* Harvey P. Dale, Oct 24 2021 *)

PARI

a(n)=if(n==Mod(5,6),return(0));k=1;while(!isprime(k^n+k-1),k++);k
vector(100,n,a(n))