A049246 Smallest nonnegative value taken on by 7x^2 - ny^2 for an infinite number of integer pairs (x, y).

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

Offset

1,1

Links

Table of n, a(n) for n=1..105.

Mathematica

p = 7; 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], Switch[n, 64 | 81, z = p; fz = $Aborted, _, 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, 105}] (* Jean-François Alcover, Oct 11 2016 *)

Crossrefs

Sequence in context: A350882 A230407 A137759 * A231186 A021078 A130793

Adjacent sequences: A049243 A049244 A049245 * A049247 A049248 A049249

Keyword

nonn

Author

David W. Wilson

Status

approved