A049265 Smallest nonnegative value taken on by n*x^2 - 6*y^2 for an infinite number of integer pairs (x, y).

1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 3, 6, 7, 2, 6, 10, 3, 12, 3, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 1, 8, 3, 10, 11, 12, 13, 2, 6, 10, 3, 18, 3, 12, 21, 10, 23, 24, 1, 26, 27, 28, 29, 0, 1, 2, 3, 4, 3, 6, 7, 2, 9, 10, 11, 12, 3, 12, 15, 16, 17, 18, 19, 2, 6, 10, 14, 6, 1, 26, 3, 12, 3, 30, 10, 2

Offset

1,2

Links

Table of n, a(n) for n=1..86.

Mathematica

p = 6; 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, 86}] (* Jean-François Alcover, Oct 11 2016 *)

Crossrefs

Sequence in context: A303534 A369183 A030567 * A010875 A260187 A257687

Adjacent sequences: A049262 A049263 A049264 * A049266 A049267 A049268

Keyword

nonn

Author

David W. Wilson, Dec 11 1999

Status

approved