A234972 Least prime p < prime(n) such that 2^p - 1 is a primitive root modulo prime(n), or 0 if such a prime p does not exist.

0, 0, 2, 2, 3, 3, 2, 2, 3, 2, 2, 17, 3, 2, 5, 2, 5, 3, 3, 3, 5, 2, 11, 2, 3, 2, 13, 3, 7, 2, 2, 5, 2, 2, 2, 3, 11, 2, 11, 2, 3, 7, 7, 7, 2, 2, 2, 2, 5, 3, 2, 3, 3, 7, 2, 3, 2, 11, 5, 2, 2, 2, 5, 5, 5, 2, 2, 5, 3, 3, 2, 3, 7, 7, 2, 7, 2, 3, 2, 7, 5, 31, 3, 3, 5, 3, 2, 5, 2, 2, 5, 5, 2, 3, 3, 5, 2, 2, 7, 7

Offset

1,3

Comments

Conjecture: a(n) > 0 for all n > 2.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..2000

Example

a(3) = 2 since 2 is a prime smaller than prime(3) = 5 with 2^2 - 1 = 3 a primitive root modulo prime(3) = 5.

Mathematica

gp[g_, p_]:=Mod[g, p]>0&&(Length[Union[Table[Mod[g^k, p], {k, 1, p-1}]]]==p-1)
Do[Do[If[gp[2^(Prime[k])-1, Prime[n]], Print[n, " ", Prime[k]]; Goto[aa]], {k, 1, n-1}]; Print[n, " ", 0]; Label[aa]; Continue, {n, 1, 100}]

Crossrefs

Cf. A000040, A001348, A001918.

Sequence in context: A071820 A055092 A213202 * A367007 A130326 A059906

Adjacent sequences: A234969 A234970 A234971 * A234973 A234974 A234975

Keyword

nonn

Author

Zhi-Wei Sun, Apr 20 2014

Status

approved