A242750 Positive integers n with property that n is a primitive root modulo prime(n).

1, 2, 3, 6, 7, 10, 11, 13, 15, 18, 24, 26, 28, 33, 39, 41, 44, 45, 48, 50, 54, 55, 56, 58, 62, 65, 68, 69, 71, 75, 79, 83, 85, 93, 95, 107, 108, 109, 110, 117, 118, 119, 120, 123, 126, 129, 130, 131, 133, 139, 142, 143, 145, 148, 157, 158, 160, 163, 164, 166, 170, 172, 173, 174, 179, 182, 186, 190, 191, 195

Offset

1,2

Comments

According to the conjecture in A242748, this sequence should have infinitely many terms.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Example

6 is a member since 6 is a primitive root modulo prime(6) = 13, but 4 and 5 are not since 4 is not a primitive root modulo prime(4) = 7 and 5 is not a primitive root modulo prime(5) = 11.

Mathematica

dv[n_]:=Divisors[n]
n=0; Do[Do[If[Mod[k^(Part[dv[Prime[k]-1], j]), Prime[k]]==1, Goto[aa]], {j, 1, Length[dv[Prime[k]-1]]-1}]; n=n+1; Print[n, " ", k]; Label[aa]; Continue, {k, 1, 195}]

Crossrefs

Cf. A000040, A000720, A242748, A242752.

Sequence in context: A307414 A073439 A188084 * A299239 A335033 A107998

Adjacent sequences: A242747 A242748 A242749 * A242751 A242752 A242753

Keyword

nonn

Author

Zhi-Wei Sun, May 21 2014

Status

approved