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A243655 Positive numbers that are primitively represented by the indefinite quadratic form x^2 - 3y^2 of discriminant 12. 7
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Oct 31 2016 *)

CROSSREFS

Cf. A084916 (all numbers represented), A068228.

Sequence in context: A056115 A173358 A101247 * A072212 A028872 A049718

Adjacent sequences:  A243652 A243653 A243654 * A243656 A243657 A243658

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jun 11 2014

STATUS

approved

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Last modified December 16 07:41 EST 2017. Contains 296076 sequences.