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.
From Klaus Purath, May 07 2023: (Start)
Also, positive integers of the form x^2 + (2m+1)xy + (m^2+m-3)y^2, m, x, y integers. This includes the form in the name.
Also, positive integers of the form x^2 + 2mxy + (m^2-13)y^2, m, x, y integers. This includes the form in the comment above.
This sequence contains all squares. The prime factors of the terms except for {2, 5, 7, 11, 19, ...} = A038884 are terms of the sequence. Also the products of terms belong to the sequence. Thus this set of terms is closed under multiplication.
LINKS
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
Entry revised by N. J. A. Sloane, Jun 01 2014
STATUS
approved