A141339 Primes of the form -x^2+9*x*y+3*y^2 (as well as of the form 11*x^2+15*x*y+3*y^2).

3, 11, 17, 23, 29, 53, 83, 89, 137, 167, 179, 197, 239, 251, 263, 269, 347, 353, 383, 389, 401, 449, 461, 491, 509, 557, 569, 587, 641, 647, 677, 719, 743, 761, 773, 797, 809, 821, 827, 863, 881, 911, 929, 941, 947, 953, 983, 1013, 1019, 1049, 1091, 1097

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(5) = 29 because we can write 29 = -1^2 + 9*1*2 + 3*2^2 (or 29 = 11*1^2 + 15*1*1 + 3*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. A141338 (d=93).

Extensions

More terms from Colin Barker, Apr 05 2015