A049264 Smallest nonnegative value taken on by n*x^2 - 5*y^2 for an infinite number of integer pairs (x, y).

1, 2, 3, 4, 0, 1, 2, 3, 1, 5, 6, 3, 5, 1, 10, 11, 3, 13, 14, 0, 1, 2, 2, 4, 5, 5, 7, 7, 5, 10, 11, 3, 7, 5, 15, 4, 5, 2, 19, 20, 9, 22, 23, 24, 0, 1, 2, 3, 1, 5, 6, 7, 3, 1, 10, 4, 3, 5, 6, 15, 16, 3, 7, 11, 5, 19, 22, 3, 1, 25, 11, 27, 5, 5, 30, 31, 7, 33, 34, 0, 1, 2, 3, 4, 5, 1, 7, 8, 5, 10, 11

Offset

1,2

Links

Table of n, a(n) for n=1..91.

Mathematica

p = 5; f[n_, z_] := FindInstance[x > 0 && y > 0 && n*x^2 - p*y^2 == z, {x, y}, Integers, 1]; a[n_] := For[z = 0, True, z = z + GCD[n, p], 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, 91}] (* Jean-François Alcover, Oct 11 2016 *)

Crossrefs

Sequence in context: A031235 A090141 A378366 * A010874 A330358 A278182

Adjacent sequences: A049261 A049262 A049263 * A049265 A049266 A049267

Keyword

nonn

Author

David W. Wilson

Status

approved