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 A003626 Inert rational primes in Q(sqrt(-5)). (Formerly M4769) 2

%I M4769

%S 11,13,17,19,31,37,53,59,71,73,79,97,113,131,137,139,151,157,173,179,

%T 191,193,197,199,211,233,239,251,257,271,277,293,311,313,317,331,337,

%U 353,359,373,379,397,419,431,433,439,457,479,491,499,557,571,577,593,599

%N Inert rational primes in Q(sqrt(-5)).

%C Primes congruent to 11, 13, 17, 19 (mod 20). - Michael Somos, Aug 14 2012

%D H. Hasse, Number Theory, Springer-Verlag, NY, 1980, p. 498.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Vincenzo Librandi, <a href="/A003626/b003626.txt">Table of n, a(n) for n = 1..5000</a>

%t Select[Prime[Range[1000]],MemberQ[{11,13,17,19},Mod[#,20]]&] (* _Vincenzo Librandi_, Aug 20 2012 *)

%o (PARI) {a(n) = local( cnt, m ); if( n<1, return( 0 )); while( cnt < n, if( isprime( m++) && kronecker( -20, m )==-1, cnt++ )); m} /* Michael Somos, Aug 14 2012 */

%K nonn,nice

%O 1,1

%A _N. J. A. Sloane_, Mira Bernstein

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