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
Keywords
Links
- 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)
Programs
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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 *)
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