cp's OEIS Frontend

A213051 Primes of the form 4*k+3 with primitive root +2.

%I A213051 #22 Oct 11 2021 04:38:26
%S A213051 3,11,19,59,67,83,107,131,139,163,179,211,227,347,379,419,443,467,491,
%T A213051 523,547,563,587,619,659,787,827,859,883,907,947,1019,1091,1123,1171,
%U A213051 1187,1259,1283,1291,1307,1427,1451,1483,1499,1523,1531,1571,1619,1667,1747
%N A213051 Primes of the form 4*k+3 with primitive root +2.
%C A213051 Primes with primitive root +2 where -2 is not a primitive root.
%C A213051 A001122 is the union of A213050 and A213051.
%H A213051 Amiram Eldar, <a href="/A213051/b213051.txt">Table of n, a(n) for n = 1..10000</a>
%H A213051 Christian Elsholtz, <a href="http://arxiv.org/abs/1602.05974">Almost all primes have a multiple of small Hamming weight</a>, arXiv:1602.05974 [math.NT], 2016. See p. 6.
%t A213051 Select[Prime[Range[300]], Mod[#, 4] == 3 && PrimitiveRoot[#, 2] == 2&] (* _Jean-François Alcover_, Jul 22 2018 *)
%o A213051 (PARI)
%o A213051 { forprime (p=3, 10^4,
%o A213051     rp = znorder(Mod(+2,p));
%o A213051     rm = znorder(Mod(-2,p));
%o A213051     if ( (rp==p-1) && (rm!=p-1), print1(p,", ") );
%o A213051 );}
%Y A213051 Cf. A213050 (primes 4*k+1 with primitive root +2), A001122 (primitive root +2).
%K A213051 nonn
%O A213051 1,1
%A A213051 _Joerg Arndt_, Jun 03 2012