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A213050 Primes of the form 4*k+1 with primitive root +2. 2

%I

%S 5,13,29,37,53,61,101,149,173,181,197,269,293,317,349,373,389,421,461,

%T 509,541,557,613,653,661,677,701,709,757,773,797,821,829,853,877,941,

%U 1061,1109,1117,1213,1229,1237,1277,1301,1373,1381,1453,1493,1549,1621

%N Primes of the form 4*k+1 with primitive root +2.

%C Primes p such that both +2 and -2 are primitive roots mod p.

%C A001122 == A213050 union A213051.

%t Select[Prime[Range[300]], Mod[#, 4] == 1 && PrimitiveRoot[#, 2] == 2&] (* _Jean-Fran├žois Alcover_, Jul 22 2018 *)

%o (PARI)

%o { forprime (p=3, 10^4,

%o rp = znorder(Mod(+2,p));

%o rm = znorder(Mod(-2,p));

%o if ( (rp==p-1) && (rm==p-1), print1(p,", ") );

%o );}

%Y Cf. A213051 (primes 4*k+3 with primitive root +2).

%Y Cf. A001122 (primitive root +2), A007885 (primitive root +2 or -2).

%K nonn

%O 1,1

%A _Joerg Arndt_, Jun 03 2012

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Last modified August 13 22:34 EDT 2020. Contains 336465 sequences. (Running on oeis4.)