A142955 Primes of the form 3*x^2 + 4*x*y - 5*y^2 (as well as of the form 3*x^2 + 10*x*y + 2*y^2).

2, 3, 19, 31, 59, 67, 71, 79, 103, 107, 127, 151, 167, 179, 211, 223, 227, 307, 331, 379, 383, 431, 439, 487, 523, 547, 563, 599, 607, 659, 683, 743, 751, 787, 811, 827, 839, 863, 887, 907, 911, 971, 983, 991, 1019, 1039, 1063, 1091, 1123, 1171, 1231, 1283

Offset

1,1

Comments

Discriminant = 76. 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(4) = 31 because we can write 31 = 3*3^2 + 4*3*2 - 5*2^2 (or 31 = 3*1^2 + 10*1*2 + 2*2^2).

Crossrefs

Cf. A142956 (d=76). A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17). A141111, A141112 (d=65).

Sequence in context: A265799 A058912 A040145 * A213896 A088790 A283186

Adjacent sequences: A142952 A142953 A142954 * A142956 A142957 A142958

Keyword

nonn

Author

Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (laucabfer(AT)alum.us.es), Jul 14 2008

Extensions

More terms from Colin Barker, Apr 05 2015

Edited by M. F. Hasler, Feb 18 2022

Status

approved