A141337 Primes of the form -2*x^2+6*x*y+7*y^2 (as well as of the form 14*x^2+22*x*y+7*y^2).

7, 11, 19, 23, 43, 67, 79, 83, 103, 107, 191, 199, 227, 251, 263, 283, 359, 367, 379, 383, 419, 431, 467, 479, 503, 523, 563, 571, 619, 631, 643, 659, 727, 743, 751, 787, 827, 839, 907, 911, 919, 971, 983, 1019, 1031, 1063, 1091, 1103, 1123, 1171, 1187, 1259

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(5)=43 because we can write 43=-2*10^2+6*10*3+7*3^2 (or 14*1^2+22*1*1+7*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. A141336 (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