A243706 Primes represented by the indefinite quadratic form 3x^2+13xy-3y^2.

3, 7, 13, 17, 47, 53, 67, 97, 137, 157, 167, 193, 227, 233, 257, 263, 293, 313, 317, 347, 383, 397, 457, 463, 503, 547, 557, 563, 577, 587, 593, 643, 653, 673, 683, 727, 757, 773, 823, 827, 883, 887, 937, 967, 977, 997, 1013, 1063, 1093

Offset

1,1

Comments

Discriminant 205.

12*a(n) has the form z^2 - 205*y^2, where z = 6*x+13*y. [Bruno Berselli, Jun 20 2014]

Links

Table of n, a(n) for n=1..49.

N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Prog

(PARI)
fc(a, b, c, M) = {
my(t1=List(), t2);
forprime(p=2, prime(M),
t2 = qfbsolve(Qfb(a, b, c), p);
if(t2 != 0, listput(t1, p))
);
Vec(t1)
};
fc(3, 13, -3, 600)

Crossrefs

Primes in A243705.

Sequence in context: A214782 A032437 A076746 * A214696 A291661 A310256

Adjacent sequences: A243703 A243704 A243705 * A243707 A243708 A243709

Keyword

nonn

Author

N. J. A. Sloane, Jun 17 2014

Status

approved