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

1,1

Comments

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

Links

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

Example

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

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}]

Crossrefs

Cf. A000040, A000720, A242748, A242750.

Sequence in context: A186945 A193761 A215355 * A215813 A235638 A227829

Adjacent sequences: A242749 A242750 A242751 * A242753 A242754 A242755

Keyword

nonn

Author

Zhi-Wei Sun, May 21 2014

Status

approved