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%I #25 Feb 18 2022 16:11:32
%S 5,11,29,41,59,71,89,101,131,149,179,191,239,251,269,281,311,359,389,
%T 401,419,431,449,461,479,491,509,521,569,599,641,659,701,719,761,809,
%U 821,839,881,911,929,941,971,1019,1031,1049,1061,1091,1109,1151,1181,1229,1259
%N Primes of the form -x^2 + 5*x*y + 5*y^2 (as well as of the form 9*x^2 + 15*x*y + 5*y^2).
%C Discriminant = 45. Class = 2. Binary quadratic forms a*x^2 + b*x*y + c*y^2 have discriminant d = b^2 - 4ac.
%D Z. I. Borevich and I. R. Shafarevich, Number Theory.
%H Juan Arias-de-Reyna, <a href="/A141785/b141785.txt">Table of n, a(n) for n = 1..10000</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(2) = 29 because we can write 29 = -1^2 + 5*1*2 + 5*2^2 (or 29 = 9*1^2 + 15*1*1 + 5*1^2)
%t Select[Prime[Range[250]], # == 5 || MatchQ[Mod[#, 45], Alternatives[11, 14, 26, 29, 41, 44]]&] (* _Jean-François Alcover_, Oct 28 2016 *)
%Y Cf. A033212 (d=45), A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17): A141111, A141112 (d=65).
%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