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%I M4356 N1825 #59 Feb 13 2023 11:16:43
%S 7,17,31,43,79,89,113,127,137,199,223,233,257,281,283,331,353,401,449,
%T 463,487,521,569,571,593,607,617,631,641,691,739,751,809,811,823,857,
%U 881,929,953,977,1013,1039,1049,1063,1087,1097,1193,1217
%N Primes with 3 as smallest primitive root.
%D 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.
%D M. Kraitchik, Recherches sur la Théorie des Nombres. Gauthiers-Villars, Paris, Vol. 1, 1924, Vol. 2, 1929, see Vol. 1, p. 57.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H T. D. Noe, <a href="/A001123/b001123.txt">Table of n, a(n) for n = 1..1000</a>
%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%H <a href="/index/Pri#primes_root">Index entries for primes by primitive root</a>
%t Prime[ Select[ Range[200], PrimitiveRoot[ Prime[ # ]] == 3 & ]]
%t (* or *)
%t Select[ Prime@Range@200, PrimitiveRoot@# == 3 &] (* _Robert G. Wilson v_, May 11 2001 *)
%o (PARI) forprime(p=3, 1000, if(znorder(Mod(2, p))!=p-1&&znorder(Mod(3, p))==p-1, print1(p,", ")));
%o (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
%o (Python)
%o from itertools import islice
%o from sympy import nextprime, is_primitive_root
%o def A001123_gen(): # generator of terms
%o p = 3
%o while (p:=nextprime(p)):
%o if not is_primitive_root(2,p) and is_primitive_root(3,p):
%o yield p
%o A001123_list = list(islice(A001123_gen(),30)) # _Chai Wah Wu_, Feb 13 2023
%Y Cf. A001122, A001124, etc.
%Y Cf. A019334.
%K nonn
%O 1,1
%A _N. J. A. Sloane_
%E More terms from _Robert G. Wilson v_, May 10 2001
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