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%I #32 Feb 18 2022 15:30:25
%S 3,7,19,31,47,59,83,103,131,139,167,199,223,227,251,271,283,307,311,
%T 367,383,419,439,467,479,503,523,563,587,607,619,643,647,691,719,727,
%U 787,811,839,859,887,971,983,1039,1063,1091,1123,1151,1223,1231,1259,1279,1291,1307,1319,1399,1427
%N Primes of the form -2*x^2+2*x*y+3*y^2 (as well as of the form 6*x^2+10*x*y+3*y^2).
%C Discriminant = 28. Class = 2. Binary quadratic forms a*x^2 + b*x*y + c*y^2 have discriminant d = b^2 - 4ac.
%C Also primes of form 7*u^2-v^2. The transformation {u,v}={-x-y,3*x+2*y} yields the form in the title. [_Juan Arias-de-Reyna_, Mar 19 2011]
%C This is also the list of primes p such that p = 7 or p is congruent to 3, 19 or 27 mod 28. - _Jean-François Alcover_, Oct 28 2016
%D Z. I. Borevich and I. R. Shafarevich, Number Theory.
%H Juan Arias-de-Reyna, <a href="/A141173/b141173.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(3)=19 because we can write 19=-2*4^2+2*4*3+3*3^2 (or 19=6*1^2+10*1*1+3*1^2).
%t Select[Prime[Range[250]], # == 7 || MatchQ[Mod[#, 28], 3|19|27]&] (* _Jean-François Alcover_, Oct 28 2016 *)
%Y Cf. A141172 (d=28) A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17): A141111, A141112 (d=65).
%Y Cf. also A242666.
%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 (lourdescm84(AT)hotmail.com), Jun 12 2008
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