A248220 Values of n such that the equation x^2 - n*y^2 = n*(n+1)*(n+2)/6 has integer solutions.

1, 2, 4, 7, 14, 16, 25, 31, 39, 48, 49, 52, 57, 64, 73, 74, 79, 84, 86, 97, 100, 112, 121, 127, 129, 134, 169, 192, 194, 196, 199, 217, 241, 244, 254, 256, 266, 273, 289, 292, 302, 304, 326, 336, 337, 350, 361, 372, 399, 400, 409, 448, 457, 484, 487, 489, 511

Offset: 1

Author

Colin Barker, Oct 04 2014

Keywords

• nonn

Examples

			7 is in the sequence because x^2-7*y^2=84 has integer solutions, including (x,y) = (14,4) and (28,10).
		

Crossrefs

Cf. A000292, A134419, A245226, A248194.

Programs

Mathematica

Select[Range[300],Length[FullSimplify[Solve[x^2-#*y^2==#*(#+1)*(#+2)/6,{x,y},Integers]/.C[1]->1]]>0&] (* Vaclav Kotesovec, Oct 05 2014, Mathematica version >= 8 *)

Extensions

More terms from Vaclav Kotesovec, Oct 05 2014