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%I #23 Oct 25 2016 14:29:27
%S 3,11,23,47,59,71,83,107,131,167,179,191,227,239,251,263,311,347,359,
%T 383,419,431,443,467,479,491,503,563,587,599,647,659,683,719,743,827,
%U 839,863,887,911,947,971,983,1019,1031,1091,1103,1151,1163,1187,1223
%N Primes of the form -x^2+6*x*y+3*y^2 (as well as of the form 8*x^2+12*x*y+3*y^2).
%C Discriminant = 48. Class = 2. Binary quadratic forms a*x^2+b*x*y+c*y^2 have discriminant d=b^2-4ac and gcd(a,b,c)=1.
%C Values of the quadratic form are {0,3,8,11} mod 12, so all values with the exception of 3 are also in A068231. - _R. J. Mathar_, Jul 30 2008
%C Is this the same sequence (apart from the initial 3) as A068231?
%D Z. I. Borevich and I. R. Shafarevich, Number Theory. Academic Press, NY, 1966.
%D D. B. Zagier, Zetafunktionen und quadratische Körper, Springer, 1981.
%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)
%e a(3)=23 because we can write 23= -1^2+6*1*2+3*2^2 (or 23=8*1^2+12*1*1+3*1^2).
%t Reap[For[p = 2, p < 2000, p = NextPrime[p], If[FindInstance[p == -x^2 + 6*x*y + 3*y^2, {x, y}, Integers, 1] =!= {}, Print[p]; Sow[p]]]][[2, 1]] (* _Jean-François Alcover_, Oct 25 2016 *)
%Y Cf. A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17). A141111, A141112 (d=65). A068228 (d=48).
%Y Cf. A243169.
%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 (sergarmor(AT)yahoo.es), Jun 12 2008
%E More terms from _Colin Barker_, Apr 05 2015
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