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

Author

David W. Wilson

Keywords

• nonn

Programs

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 *)