A049260 Smallest nonnegative value taken on by n*x^2 - y^2 for an infinite number of integer pairs (x, y).

0, 1, 2, 0, 1, 2, 3, 4, 0, 1, 2, 3, 1, 5, 6, 0, 1, 2, 2, 4, 3, 2, 7, 8, 0, 1, 2, 3, 1, 5, 3, 7, 8, 9, 10, 0, 1, 2, 3, 4, 1, 6, 2, 7, 5, 5, 11, 12, 0, 1, 2, 3, 1, 2, 6, 7, 3, 1, 2, 11, 1, 13, 14, 0, 1, 2, 2, 4, 5, 5, 7, 8, 1, 1, 11, 3, 7, 14, 15, 16, 0, 1, 2, 3, 1, 2, 6, 7, 1, 9, 3, 7, 3, 5, 14, 15, 1

Offset

1,3

Links

Table of n, a(n) for n=1..97.

Mathematica

f[n_, z_] := FindInstance[x > 0 && y > 0 && n*x^2 - y^2 == z, {x, y}, Integers, 1]; a[n_] := For[z = 0, True, z++, fz = f[n, z]; If[fz =!= {}, Print["a(", n, ") = ", z, " {x, y} = ", {x, y} /. fz[[1]]]; Return[z]]]; Array[a, 97] (* Jean-François Alcover, Oct 11 2016 *)

Crossrefs

Sequence in context: A318601 A306814 A241382 * A273294 A053186 A066628

Adjacent sequences: A049257 A049258 A049259 * A049261 A049262 A049263

Keyword

nonn

Author

David W. Wilson

Status

approved