A243655 Positive numbers that are primitively represented by the indefinite quadratic form x^2 - 3y^2 of discriminant 12.

1, 6, 13, 22, 33, 37, 46, 61, 69, 73, 78, 94, 97, 109, 118, 121, 141, 142, 157, 166, 169, 177, 181, 193, 213, 214, 222, 229, 241, 249, 253, 262, 277, 286, 313, 321, 334, 337, 349, 358, 366, 373, 382, 393, 397, 409, 421, 429, 433, 438, 454, 457, 478, 481

Offset

1,2

Comments

x^2+2xy-2y^2 is an equivalent form.

Links

Table of n, a(n) for n=1..54.

Will Jagy, C++ program Conway_Positive_All.cc to find all positive numbers represented by an indefinite binary quadratic form

Will Jagy, Sample output from Conway_Positive_All.cc

Will Jagy, C++ program Conway_Positive_Primitive.cc to find positive numbers primitively represented by an indefinite binary quadratic form

Will Jagy, Sample output from Conway_Positive_Prim.cc

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

Mathematica

Reap[For[n = 1, n < 500, n++, r = Reduce[x^2 - 3 y^2 == n, {x, y}, Integers]; If[r =!= False, If[AnyTrue[{x, y} /. {ToRules[r /. C[1] -> 0]}, CoprimeQ @@ # &], Print[n]; Sow[n]]]]][[2, 1]] (* Jean-François Alcover, Oct 31 2016 *)

Crossrefs

Cf. A084916 (all numbers represented), A068228.

Sequence in context: A056115 A173358 A101247 * A377607 A072212 A028872

Adjacent sequences: A243652 A243653 A243654 * A243656 A243657 A243658

Keyword

nonn

Author

N. J. A. Sloane, Jun 11 2014

Status

approved