A049249 Smallest nonnegative value taken on by 10x^2 - ny^2 for an infinite number of integer pairs (x, y).

1, 2, 7, 4, 5, 4, 3, 2, 1, 0, 10, 10, 3, 10, 10, 10, 7, 10, 10, 10, 6, 2, 10, 10, 10, 10, 7, 10, 10, 10, 1, 8, 7, 6, 5, 4, 3, 2, 1, 0, 10, 10, 10, 10, 10, 10, 10, 10, 6, 10, 10, 10, 10, 4, 10, 10, 10, 10, 10, 10, 6, 2, 10, 10, 10, 6, 10, 10, 10, 10, 1, 10, 10, 10, 10, 10, 10, 10, 1, 10

Offset

1,2

Links

Table of n, a(n) for n=1..80.

Mathematica

p = 10; f[n_, z_] := FindInstance[x > 0 && y > 0 && p*x^2 - n*y^2 == z, {x, y}, Integers, 1]; a[n_] := For[z = 0, z <= p, z = z + GCD[n, p], Which[n == 64, z = 10; fz = $Aborted, True, fz = TimeConstrained[f[n, z], 300]]; fz = If[fz === $Aborted, {{x -> Null, y -> Null}}, fz]; If[fz =!= {}, Print["a(", n, ") = ", z, " {x, y} = ", {x, y} /. fz[[1]]]; Return[z]]]; Table[a[n], {n, 1, 80}] (* Jean-François Alcover, Oct 11 2016 *)

Crossrefs

Sequence in context: A323755 A093590 A065629 * A336000 A222237 A347767

Adjacent sequences: A049246 A049247 A049248 * A049250 A049251 A049252

Keyword

nonn

Author

David W. Wilson

Status

approved