

A001123


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


11



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
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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 ThÃ©orie des Nombres. GauthiersVillars, 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))!=p1&&znorder(Mod(3, p))==p1, print1(p, ", ")));
(PARI) { n=0; forprime (p=3, 99999, if (znorder(Mod(2, p))!=p1 && znorder(Mod(3, p))==p1, n++; write("b001123.txt", n, " ", p); if (n>=1000, break) ) ) } \\ Harry J. Smith, Jun 14 2009


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



