A019353 - OEIS

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

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OFFSET

1,1

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

MATHEMATICA

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

PROG

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

CROSSREFS

Cf. A019334, A005596, A000720, A323594.

Sequence in context: A077217 A120847 A244085 * A106882 A172122 A101009

Adjacent sequences: A019350 A019351 A019352 * A019354 A019355 A019356

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved