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%I M4769 #26 May 22 2022 09:43:23
%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
%C Legendre symbol (-5, a(n)) = -1. For prime 5 this symbol is set to 0, and for other odd primes (-5, prime) = +1, given in A139513. - _Wolfdieter Lang_, Mar 05 2021
%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>
%H R. G. Wilson, V, <a href="/A007376/a007376.pdf">Letter to N. J. A. Sloane, Oct. 1993</a>
%H <a href="https://oeis.org/index/Pri#primes_decomp_of">Index to sequences related to decomposition of primes in quadratic fields</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 */
%Y Cf. A139513.
%K nonn,nice
%O 1,1
%A _N. J. A. Sloane_, _Mira Bernstein_
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