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%I #29 Feb 18 2022 15:38:07
%S 2,11,43,67,107,113,137,163,179,193,211,233,281,331,337,347,379,401,
%T 443,449,457,491,499,547,569,571,617,641,659,673,683,739,809,827,883,
%U 907,947,953,977,1009,1019,1033,1051,1129,1163,1171,1187,1201,1283,1289
%N Primes of the form 2*x^2+4*x*y-5*y^2 (as well as of the form 2*x^2+8*x*y+y^2).
%C Discriminant = 56. Class = 2. Binary quadratic forms a*x^2 + b*x*y + c*y^2 have discriminant d = b^2 - 4ac.
%C Also primes of the form x^2 + 6xy - 5y^2, cf. A243186. - _N. J. A. Sloane_, Jun 05 2014
%D Z. I. Borevich and I. R. Shafarevich, Number Theory.
%H Vincenzo Librandi, <a href="/A141190/b141190.txt">Table of n, a(n) for n = 1..1000</a>
%H N. J. A. Sloane et al., <a href="/wiki/Binary_Quadratic_Forms_and_OEIS">Binary Quadratic Forms and OEIS</a>: Index to related sequences, programs, references. OEIS wiki, June 2014.
%H D. B. Zagier, <a href="https://doi.org/10.1007/978-3-642-61829-1">Zetafunktionen und quadratische Körper</a>, Springer, 1981.
%e a(3) = 43 is in the sequence because we can write 43 = 2*4^2 + 4*4*1 - 5*1^2, or 43 = 2*3^2 + 8*3*1 + 1^2.
%t xy[{x_, y_}]:={2 x^2 + 4 x y - 5 y^2, 2 y^2 + 4 x y - 5 x^2}; Union[Select[Flatten[xy/@Subsets[Range[50], {2}]], #>0&&PrimeQ[#]&]] (* _Vincenzo Librandi_, Jun 09 2014 *)
%Y Cf. A141191 (d=56) A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17). A141111, A141112 (d=65).
%Y Cf. A243186.
%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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