A019353 Primes with primitive root 27.

2, 5, 17, 29, 53, 89, 101, 113, 137, 149, 173, 197, 233, 257, 269, 281, 293, 317, 353, 389, 401, 449, 461, 509, 521, 557, 569, 593, 617, 641, 653, 677, 701, 773, 797, 809, 821, 857, 881, 929, 941, 953, 977, 1013, 1049, 1061, 1097, 1109, 1193, 1217, 1229, 1277, 1301

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

From Jianing Song, May 12 2024: (Start)

Members of A019334 that are not congruent to 1 mod 3. Terms greater than 2 are congruent to 5 modulo 12.

According to Artin's conjecture, the number of terms <= N is roughly ((3/5)*C)*PrimePi(N), where C is the Artin's constant = A005596, PrimePi = A000720. Compare: the number of terms of A001122 that are no greater than N is roughly C*PrimePi(N). (End)

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Wikipedia, Artin's conjecture on primitive roots
• Index entries for primes by primitive root

Crossrefs

Cf. A019334, A005596, A000720, A323594.

Programs

Mathematica

pr=27; Select[Prime[Range[300]], MultiplicativeOrder[pr, # ] == #-1 &]

PARI

isA019353(n) = isprime(n) && (n!=3) && znorder(Mod(27,n)) == n-1 \\ Jianing Song, May 12 2024