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

1,2

Links

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

Example

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

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 *)

Crossrefs

Cf. A000292, A134419, A245226, A248194.

Sequence in context: A286371 A030135 A222306 * A018476 A265309 A293825

Adjacent sequences: A248217 A248218 A248219 * A248221 A248222 A248223

Keyword

nonn

Author

Colin Barker, Oct 04 2014

Extensions

More terms from Vaclav Kotesovec, Oct 05 2014

Status

approved