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%I #18 May 20 2023 04:37:11
%S 11,59,71,131,179,191,239,251,311,359,419,431,479,491,599,659,719,839,
%T 911,971,1019,1031,1091,1151,1259,1319,1439,1451,1499,1511,1559,1571,
%U 1619,1811,1871,1931,1979,2039,2099,2111,2339,2351,2399,2411,2459,2531,2579,2591,2699,2711
%N Primes of the form -x^2+6*x*y+6*y^2 (as well as of the form 11*x^2+18*x*y+6*y^2).
%C Discriminant = 60. Class = 4. 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.
%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)=71 because we can write 71=-1^2+6*1*3+6*3^2 (or 71=11*1^2+18*1*2+6*2^2).
%t Reap[For[p = 2, p < 3000, p = NextPrime[p], If[FindInstance[p == -x^2 + 6*x*y + 6*y^2, {x, y}, Integers, 1] =!= {}, Print[p]; Sow[p]]]][[2, 1]] (* _Jean-François Alcover_, Oct 25 2016 *)
%Y Cf. A107152, A141303, A141304 (d=60).
%Y Primes in A237606.
%K nonn
%O 1,1
%A Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (oscfalgan(AT)yahoo.es), Jun 24 2008
%E Offset corrected by _Mohammed Yaseen_, May 20 2023
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