A141338 Primes of the form x^2+9*x*y-3*y^2 (as well as of the form 7*x^2+11*x*y+y^2).

7, 19, 31, 67, 97, 103, 109, 157, 163, 193, 211, 283, 307, 349, 373, 379, 397, 421, 439, 541, 547, 577, 607, 661, 691, 727, 733, 751, 769, 811, 853, 877, 907, 919, 937, 997, 1033, 1039, 1051, 1063, 1087, 1093, 1117, 1123, 1213, 1237, 1249, 1279, 1291, 1303

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 = 93. Class = 2. Binary quadratic forms a*x^2 + b*x*y + c*y^2 have discriminant d = b^2 - 4ac.

Examples

			a(2) = 19 because we can write 19 = 2^2 + 9*2*5 - 3*5^2 (or 19 = 7*1^2 + 11*1*1 + 1^2).
		

References

• Z. I. Borevich and I. R. Shafarevich, Number Theory.

Links

• N. J. A. Sloane et al., Binary Quadratic Forms and OEIS: Index to related sequences, programs, references. OEIS wiki, June 2014.
• D. B. Zagier, Zetafunktionen und quadratische Körper, Springer, 1981.

Crossrefs

Cf. A141339 (d=93).

Extensions

More terms from Colin Barker, Apr 05 2015