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 A019335 Primes with primitive root 5. 10
 2, 3, 7, 17, 23, 37, 43, 47, 53, 73, 83, 97, 103, 107, 113, 137, 157, 167, 173, 193, 197, 223, 227, 233, 257, 263, 277, 283, 293, 307, 317, 347, 353, 373, 383, 397, 433, 443, 463, 467, 503, 523, 547, 557, 563, 577, 587, 593, 607, 613, 617, 647, 653, 673, 677, 683, 727 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS To allow primes less than the specified primitive root m (here, 5) 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 Appears to be the numbers k such that the sequence 5^n mod k has period length k-1. All terms are congruent to 2 or 3 mod 5. - Gary Detlefs, May 21 2014 From Jianing Song, Apr 27 2019: (Start) If we define   Pi(N,b) = # {p prime, p <= N, p == b (mod 5)};      Q(N) = # {p prime, p <= N, p in this sequence}, then by Artin's conjecture, Q(N) ~ (20/19)*C*N/log(N) ~ (40/19)*C*(Pi(N,2) + Pi(N,3)), where C = A005596 is Artin's constant. Conjecture: if we further define    Q(N,b) = # {p prime, p <= N, p == b (mod 5), p in this sequence}, then we have:    Q(N,2) ~ (1/2)*Q(N) ~ (20/19)*C*Pi(N,2);    Q(N,3) ~ (1/2)*Q(N) ~ (20/19)*C*Pi(N,3). (End) LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Eric Weisstein's World of Mathematics, Artin's constant Wikipedia, Artin's conjecture on primitive roots MATHEMATICA pr=5; Select[Prime[Range], MultiplicativeOrder[pr, # ] == #-1 &] PROG (PARI) isok(p) = isprime(p) && (p != 5) && (znorder(Mod(5, p)) == p-1); \\ Michel Marcus, Apr 27 2019 CROSSREFS Cf. A019334-A019421. Sequence in context: A045333 A040141 A235627 * A113425 A289379 A245590 Adjacent sequences:  A019332 A019333 A019334 * A019336 A019337 A019338 KEYWORD nonn AUTHOR STATUS approved

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Last modified October 2 04:48 EDT 2022. Contains 357191 sequences. (Running on oeis4.)