A001123 Primes with 3 as smallest primitive root.

7, 17, 31, 43, 79, 89, 113, 127, 137, 199, 223, 233, 257, 281, 283, 331, 353, 401, 449, 463, 487, 521, 569, 571, 593, 607, 617, 631, 641, 691, 739, 751, 809, 811, 823, 857, 881, 929, 953, 977, 1013, 1039, 1049, 1063, 1087, 1097, 1193, 1217

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

References

• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 864.
• M. Kraitchik, Recherches sur la Théorie des Nombres. Gauthiers-Villars, Paris, Vol. 1, 1924, Vol. 2, 1929, see Vol. 1, p. 57.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
• Index entries for primes by primitive root

Crossrefs

Cf. A001122, A001124, etc.

Cf. A019334.

Programs

Mathematica

Prime[ Select[ Range[200], PrimitiveRoot[ Prime[ # ]] == 3 & ]]
(* or *)
Select[ Prime@Range@200, PrimitiveRoot@# == 3 &] (* Robert G. Wilson v, May 11 2001 *)

PARI

forprime(p=3, 1000, if(znorder(Mod(2, p))!=p-1&&znorder(Mod(3, p))==p-1, print1(p,", ")));

PARI

{ n=0; forprime (p=3, 99999, if (znorder(Mod(2,p))!=p-1 && znorder(Mod(3,p))==p-1, n++; write("b001123.txt", n, " ", p); if (n>=1000, break) ) ) } \\ Harry J. Smith, Jun 14 2009

Python

from itertools import islice
from sympy import nextprime, is_primitive_root
def A001123_gen(): # generator of terms
    p = 3
    while (p:=nextprime(p)):
        if not is_primitive_root(2,p) and is_primitive_root(3,p):
            yield p
A001123_list = list(islice(A001123_gen(),30)) # Chai Wah Wu, Feb 13 2023

Extensions

More terms from Robert G. Wilson v, May 10 2001