A076845 Least k>0 such that n^k + n - 1 is prime.

1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 16, 1, 1, 4, 3, 1, 2, 1, 1, 4, 1, 3, 2, 1, 2, 10, 1, 1, 108, 3, 1, 2, 1, 1, 2, 2, 1, 2, 1, 3, 2, 1, 2, 20, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 4, 2, 2, 7, 8, 3, 1, 2, 1, 24, 2, 1, 1, 12, 4, 3, 8, 1, 1, 4, 3, 1, 194, 3, 1, 2, 1, 2, 2, 1, 8, 2, 1, 1, 4, 2, 2, 54, 1, 1, 4, 1, 1

Offset: 2

Author

Benoit Cloitre, Nov 20 2002

Keywords

• nonn

Comments

From Robert Israel, Apr 07 2025: (Start)

No terms == 5 (mod 6), as x^k + x - 1 is divisible by x^2 - x - 1 when k == 5 (mod 6).

a(113) > 7000 if it exists. (End)

Links

• Robert Israel, Incomplete table of n, a(n) for n = 2 .. 1000. -1 denotes a value that is > 3000 if it exists.

Crossrefs

Cf. A078178, A076846.

Cf. A010051.

Programs

Haskell

a076845 n = head [k | k <- [1..], a010051'' (n ^ k + n - 1) == 1]
-- Reinhard Zumkeller, Jul 17 2014

Maple

f:= proc(n) local k;
    for k from 1 do if isprime(n^k+n-1) then return k fi od
end proc:
map(f, [$2..112]); # Robert Israel, Apr 07 2025

Mathematica

lk[n_]:=Module[{k=1},While[!PrimeQ[n^k+n-1],k++];k]; Array[lk,100,2] (* Harvey P. Dale, Jun 29 2017 *)

PARI

a(n) = {my(k=1); while(!isprime(n^k+n-1), k++); k;} \\ Michel Marcus, Nov 29 2013