A049262 Smallest nonnegative value taken on by nx^2 - 3y^2 for an infinite number of integer pairs (x, y).

1, 2, 0, 1, 2, 3, 1, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 1, 5, 9, 6, 5, 12, 13, 14, 0, 1, 2, 3, 1, 5, 6, 6, 8, 9, 1, 5, 3, 13, 6, 15, 1, 17, 18, 19, 20, 0, 1, 2, 3, 4, 2, 6, 7, 8, 6, 10, 8, 12, 1, 2, 9, 13, 17, 6, 1, 5, 21, 22, 11, 24, 25, 26, 0, 1, 2, 3, 1, 5, 6, 6, 5, 9, 10, 6, 3, 13, 6, 15, 1, 5

Offset

1,2

Links

Table of n, a(n) for n=1..92.

Mathematica

p = 3; 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, 92}] (* Jean-François Alcover, Oct 11 2016 *)

Crossrefs

Sequence in context: A080018 A079686 A005813 * A145201 A323671 A340707

Adjacent sequences: A049259 A049260 A049261 * A049263 A049264 A049265

Keyword

nonn

Author

David W. Wilson, Dec 11 1999

Status

approved