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A035256 Positive integers of the form x^2+3xy-y^2. 2
1, 3, 4, 9, 12, 13, 16, 17, 23, 25, 27, 29, 36, 39, 43, 48, 49, 51, 52, 53, 61, 64, 68, 69, 75, 79, 81, 87, 92, 100, 101, 103, 107, 108, 113, 116, 117, 121, 127, 129, 131, 139, 144, 147, 153, 156, 157, 159, 169, 172, 173, 179, 181, 183, 191, 192, 196, 199, 204, 207, 208, 211, 212, 221, 225, 233, 237, 243, 244, 251 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This is an indefinite quadratic form of discriminant 13.

Also, positive integers of the form x^2+6xy-4y^2 (an indefinite quadratic form of discriminant 52).

Also, indices of the nonzero terms in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m= 13.

LINKS

Table of n, a(n) for n=1..70.

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

MATHEMATICA

formQ[n_] := Reduce[a > 0 && b > 0 && n == a^2 + 3 a*b - b^2, {a, b}, Integers] =!= False; Select[Range[100], formQ] (* Wesley Ivan Hurt, Jun 18 2014 *)

PROG

(PARI) m=13; select(x -> x, direuler(p=2, 101, 1/(1-(kronecker(m, p)*(X-X^2))-X)), 1) \\ Fixed by Andrey Zabolotskiy, Jul 30 2020

CROSSREFS

Primes in this sequence = A038883 and A141188.

Cf. A035195.

Sequence in context: A270817 A182828 A294229 * A287400 A309758 A047075

Adjacent sequences:  A035253 A035254 A035255 * A035257 A035258 A035259

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

Entry revised by N. J. A. Sloane, Jun 01 2014

STATUS

approved

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Last modified January 25 08:01 EST 2021. Contains 340416 sequences. (Running on oeis4.)