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 A019334 Primes with primitive root 3. 25
 2, 5, 7, 17, 19, 29, 31, 43, 53, 79, 89, 101, 113, 127, 137, 139, 149, 163, 173, 197, 199, 211, 223, 233, 257, 269, 281, 283, 293, 317, 331, 353, 379, 389, 401, 449, 461, 463, 487, 509, 521, 557, 569, 571, 593, 607, 617, 631, 641, 653, 677, 691, 701, 739, 751, 773, 797 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS To allow primes less than the specified primitive root m (here, 3) 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 02 2019 From Jianing Song, Apr 27 2019: (Start) All terms except the first are congruent to 5 or 7 modulo 12. If we define   Pi(N,b) = # {p prime, p <= N, p == b (mod 12)};      Q(N) = # {p prime, 2 < p <= N, p in this sequence}, then by Artin's conjecture, Q(N) ~ C*N/log(N) ~ 2*C*(Pi(N,5) + Pi(N,7)), where C = A005596 is Artin's constant. If we further define    Q(N,b) = # {p prime, p <= N, p == b (mod 12), p in this sequence}, then we have:    Q(N,5) ~ (3/5)*Q(N) ~ (12/5)*C*Pi(N,5);    Q(N,7) ~ (2/5)*Q(N) ~ ( 8/5)*C*Pi(N,7). For example, for the first 1000 terms except for a(1) = 2, there are 593 terms == 5 (mod 12) and 406 terms == 7 (mod 12). (End) LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 J. Conde, M. Miller, J. M. Miret, K. Saurav, On the Nonexistence of Almost Moore Digraphs of Degree Four and Five, International Conference on Mathematical Computer Engineering (ICMCE-13), pp. 2-7, At VIT University, Chennai, Volume: I, 2013. J. Conde, M. Miller, J. M. Miret, K. Saurav, On the Nonexistence of Almost Moore Digraphs of Degree Four and Five, Mathematics in Computer Science, June 2015, Volume 9, Issue 2, pp 145-149. Eric Weisstein's World of Mathematics, Artin's constant Wikipedia, Artin's conjecture on primitive roots MATHEMATICA pr=3; Select[Prime[Range], MultiplicativeOrder[pr, # ] == #-1 &] PROG (PARI) isok(p) = isprime(p) && (p!=3) && (znorder(Mod(3, p))+1 == p); \\ Michel Marcus, May 12 2019 CROSSREFS Cf. A005596, A001122 (primitive root 2). Cf. A019335-A019421. Sequence in context: A174281 A301916 A038875 * A045356 A158526 A146364 Adjacent sequences:  A019331 A019332 A019333 * A019335 A019336 A019337 KEYWORD nonn AUTHOR STATUS approved

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Last modified April 19 00:03 EDT 2021. Contains 343098 sequences. (Running on oeis4.)