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Primes of the form 3*x^2 + 4*x*y - 6*y^2 (as well as of the form 3*x^2 + 10*x*y + y^2).
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%I #14 Feb 18 2022 16:12:04

%S 3,11,59,67,89,97,113,137,163,179,251,257,313,331,353,379,401,419,433,

%T 443,449,467,499,521,577,587,617,619,641,643,683,691,859,881,883,907,

%U 929,947,971,977,1049,1123,1153,1171,1193,1259,1291,1307,1321,1409,1433

%N Primes of the form 3*x^2 + 4*x*y - 6*y^2 (as well as of the form 3*x^2 + 10*x*y + y^2).

%C Discriminant = 88. 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 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(1)=3 because we can write 3=3*1^2+4*1*0-6*0^2 (or 3=3*1^2+10*1*0+0^2).

%Y Cf. A141777 (d=88).

%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), Jul 04 2008

%E More terms from _Colin Barker_, Apr 05 2015