A141336 Primes of the form 2*x^2+6*x*y-7*y^2 (as well as of the form 2*x^2+10*x*y+y^2).

2, 13, 29, 41, 73, 101, 173, 193, 197, 233, 257, 269, 277, 317, 349, 353, 397, 409, 449, 461, 509, 541, 577, 593, 601, 653, 673, 761, 809, 821, 829, 853, 857, 877, 929, 997, 1013, 1021, 1061, 1093, 1097, 1117, 1129, 1153, 1181, 1237, 1277, 1289, 1297, 1301

Offset: 1

Author

Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (oscfalgan(AT)yahoo.es), Jun 25 2008

Keywords

• nonn

Comments

Discriminant = 92. 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.

Examples

			a(2)=13 because we can write 13=2*2^2+6*2*1-7*1^2 (or 13=2*1^2+10*1*1+1^2).
		

References

• Z. I. Borevich and I. R. Shafarevich, Number Theory. Academic Press, NY, 1966.
• D. B. Zagier, Zetafunktionen und quadratische Körper, Springer, 1981.

Crossrefs

Cf. A141337 (d=92).

Programs

Mathematica

Reap[For[p = 2, p < 2000, p = NextPrime[p], If[FindInstance[p == 2*x^2 + 6*x*y - 7*y^2, {x, y}, Integers, 1] =!= {}, Print[p]; Sow[p]]]][[2, 1]] (* Jean-François Alcover, Oct 25 2016 *)

Extensions

More terms from Colin Barker, Apr 05 2015