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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. 9
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 (list; graph; refs; listen; history; text; internal format)
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 * A130326 A059906 A112046

Adjacent sequences:  A234969 A234970 A234971 * A234973 A234974 A234975

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Apr 20 2014

STATUS

approved

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Last modified February 20 01:06 EST 2018. Contains 299357 sequences. (Running on oeis4.)