A049261 Smallest nonnegative value taken on by nx^2 - 2y^2 for an infinite number of integer pairs (x, y).

1, 0, 1, 2, 2, 4, 5, 0, 1, 2, 1, 4, 2, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 2, 2, 1, 10, 2, 12, 13, 0, 1, 2, 3, 4, 2, 4, 7, 8, 2, 6, 1, 4, 13, 14, 5, 16, 17, 0, 1, 2, 2, 4, 5, 6, 1, 2, 1, 10, 2, 6, 7, 14, 2, 16, 1, 18, 19, 20, 21, 0, 1, 2, 3, 4, 3, 6, 7, 8, 1, 2, 1, 12, 2, 4, 10, 14, 1, 10, 19, 10, 3, 22

Offset

1,4

Links

Table of n, a(n) for n=1..94.

Mathematica

p = 2; 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, 94}] (* Jean-François Alcover, Oct 11 2016 *)

Crossrefs

Sequence in context: A322253 A059372 A161422 * A135018 A073018 A201509

Adjacent sequences: A049258 A049259 A049260 * A049262 A049263 A049264

Keyword

nonn

Author

David W. Wilson, Dec 11 1999

Status

approved