A229848 Values of n such that the equation x^2 - 3*n*y^2 = n has integer solutions.

1, 4, 7, 9, 13, 16, 19, 25, 28, 31, 36, 37, 43, 49, 52, 61, 63, 64, 67, 76, 79, 81, 91, 100, 103, 109, 112, 117, 121, 124, 127, 139, 144, 148, 151, 157, 163, 169, 171, 172, 175, 181, 193, 196, 199, 208, 211, 217, 223, 225, 229, 244, 247, 252, 256, 268, 271

Offset

1,2

Links

Table of n, a(n) for n=1..57.

Example

37 appears in the sequence because the equation x^2 - 111*y^2 = 37 has integer solutions.

Mathematica

Select[Range[300], Length[FullSimplify[Solve[x^2-3*#*y^2==#, {x, y}, Integers]/.C[1]->1]]>0&] (* Vaclav Kotesovec, Oct 08 2013 *)

Crossrefs

Cf. A172000, A227939

Sequence in context: A230240 A243175 A352272 * A239993 A332335 A310961

Adjacent sequences: A229845 A229846 A229847 * A229849 A229850 A229851

Keyword

nonn

Author

Colin Barker, Oct 07 2013

Status

approved