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

1,1

Comments

Discriminant = 93. 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..50.

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

Crossrefs

Cf. A141339 (d=93).

Sequence in context: A212492 A374535 A234310 * A237366 A216531 A216564

Adjacent sequences: A141335 A141336 A141337 * A141339 A141340 A141341

Keyword

nonn

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

Extensions

More terms from Colin Barker, Apr 05 2015

Status

approved