A001123 Primes with 3 as smallest primitive root. (Formerly M4356 N1825)

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

1,1

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A001122, A001124, etc.

Cf. A019334.

Sequence in context: A228345 A196167 A290402 * A094080 A046118 A285738

Adjacent sequences: A001120 A001121 A001122 * A001124 A001125 A001126

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

Status

approved