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%I #25 Oct 30 2016 08:51:24
%S 3,7,11,37,41,47,53,67,71,73,83,101,107,127,137,139,149,151,157,173,
%T 181,197,211,223,229,233,263,269,271,293,307,317,337,349,359,367,373,
%U 379,397,419,433,443,491,509,521,571,593,599,601,613,617,619,641,659,673
%N Primes of the form 3*x^2+x*y-3*y^2 (as well as of the form 3*x^2+7*x*y+y^2).
%C Discriminant = 37. Class = 1. Binary quadratic forms a*x^2+b*x*y+c*y^2 have discriminant d=b^2-4ac and gcd(a,b,c)=1
%D Z. I. Borevich and I. R. Shafarevich, Number Theory. Academic Press, NY, 1966.
%H Jean-François Alcover, <a href="/A141178/b141178.txt">Table of n, a(n) for n = 1..10000</a>
%H N. J. A. Sloane et al., <a href="https://oeis.org/wiki/Binary_Quadratic_Forms_and_OEIS">Binary Quadratic Forms and OEIS</a> (Index to related sequences, programs, references)
%H D. B. Zagier, <a href="http://dx.doi.org/10.1007/978-3-642-61829-1">Zetafunktionen und quadratische Körper</a>, Springer-Verlag Berlin Heidelberg, 1981.
%e a(3) = 11 because we can write 11 = 3*2^2+2*1-3*1^2 (or 11 = 3*1^2+7*1*1+1^2).
%t Reap[For[p = 2, p < 1000, p = NextPrime[p], If[FindInstance[p == 3*x^2 + x*y - 3*y^2, {x, y}, Integers, 1] =!= {}, Print[p]; Sow[p]]]][[2, 1]]
%t (* or: *)
%t Select[Prime[Range[200]], # == 37 || MatchQ[Mod[#, 37], Alternatives[1, 3, 4, 7, 9, 10, 11, 12, 16, 21, 25, 26, 27, 28, 30, 33, 34, 36]]&](* _Jean-François Alcover_, Oct 25 2016, updated Oct 30 2016 *)
%Y Cf. A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17): A141111, A141112 (d=65).
%Y Primes in A035267.
%Y A subsequence of (and may possibly coincide with) A038913. - _R. J. Mathar_, Jul 22 2008
%Y For a list of sequences giving numbers and/or primes represented by binary quadratic forms, see the "Binary Quadratic Forms and OEIS" link.
%K nonn
%O 1,1
%A Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (marcanmar(AT)alum.us.es), Jun 12 2008
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