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

Author

Zhi-Wei Sun, May 21 2014

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A000040, A000720, A242748, A242752.

Programs

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}]