A242752 Primes p such that pi(p) is a primitive root modulo p, where pi(p) is the number of primes not exceeding p.

2, 3, 5, 13, 17, 29, 31, 41, 47, 61, 89, 101, 107, 137, 167, 179, 193, 197, 223, 229, 251, 257, 263, 271, 293, 313, 337, 347, 353, 379, 401, 431, 439, 487, 499, 587, 593, 599, 601, 643, 647, 653, 659, 677, 701, 727, 733, 739, 751, 797, 821, 823, 829, 857, 919, 929, 941, 967, 971, 983

Offset: 1

Author

Zhi-Wei Sun, May 21 2014

Keywords

• nonn

Comments

According to the conjecture in A232748, this sequence should contain infinitely many primes.

Examples

			a(3) = 5 since 5 is prime with pi(5) = 3 a primitive root modulo 5.
		

Links

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

Crossrefs

Cf. A000040, A000720, A242748, A242750.

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," ",Prime[k]];Label[aa];Continue,{k,1,166}]