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

1,1

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..52.

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(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).

Crossrefs

Cf. A141338 (d=93).

Sequence in context: A056983 A175073 A062284 * A069348 A165561 A038960

Adjacent sequences: A141336 A141337 A141338 * A141340 A141341 A141342

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