A141777 Primes of the form -3*x^2 + 4*x*y + 6*y^2 (as well as of the form 7*x^2 + 12*x*y + 2*y^2).

2, 7, 13, 29, 61, 79, 101, 109, 127, 149, 151, 167, 173, 197, 239, 263, 271, 277, 293, 349, 359, 373, 431, 439, 461, 479, 503, 541, 557, 607, 613, 677, 701, 733, 743, 821, 853, 877, 887, 919, 941, 967, 997, 1031, 1063, 1069, 1117, 1151, 1223, 1229, 1231

Offset

1,1

Comments

Discriminant = 88. Class = 2. Binary quadratic forms a*x^2 + b*x*y + c*y^2 have discriminant d = b^2 - 4ac.

References

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

Links

Table of n, a(n) for n=1..51.

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.

Example

a(2) = 7 because we can write 7 = -3*1^2 + 4*1*1 + 6*1^2 (= 7*1^2 + 12*1*0 + 2*0^2).

Crossrefs

Cf. A141776 (d=88).

Sequence in context: A360673 A183435 A360385 * A297883 A215206 A298215

Adjacent sequences: A141774 A141775 A141776 * A141778 A141779 A141780

Keyword

nonn

Author

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

Extensions

More terms from Colin Barker, Apr 05 2015

Status

approved