A019337 Primes with primitive root 7.

2, 5, 11, 13, 17, 23, 41, 61, 67, 71, 79, 89, 97, 101, 107, 127, 151, 163, 173, 179, 211, 229, 239, 241, 257, 263, 269, 293, 347, 349, 359, 379, 397, 431, 433, 443, 461, 491, 499, 509, 521, 547, 577, 593, 599, 601, 631, 659, 677, 683, 733, 739, 743, 761, 773, 797, 823

Offset

1,1

Comments

To allow primes less than the specified primitive root m (here, 7) to be included, we use the essentially equivalent definition "Primes p such that the multiplicative order of m mod p is p-1". This comment applies to all of A019334-A019421. - N. J. A. Sloane, Dec 03 2019

All terms apart from the first are == 5, 11, 13, 15, 17, 23 (mod 28) since 7 is a quadratic residue modulo any other prime. By Artin's conjecture, this sequence contains about 37.395% of all primes, that is, about 74.79% of all primes == 5, 11, 13, 15, 17, 23 (mod 28). - Jianing Song, Sep 05 2018

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for primes by primitive root

Mathematica

pr=7; Select[Prime[Range[200]], MultiplicativeOrder[pr, # ] == #-1 &]

Crossrefs

Cf. A167795.

Sequence in context: A066149 A215423 A019387 * A086518 A156672 A145669

Adjacent sequences: A019334 A019335 A019336 * A019338 A019339 A019340

Keyword

nonn

Author

David W. Wilson

Status

approved