A049247 Smallest nonnegative value taken on by 8x^2 - ny^2 for an infinite number of integer pairs (x, y).

4, 0, 5, 4, 3, 2, 1, 0, 8, 8, 8, 8, 8, 2, 8, 8, 4, 0, 8, 8, 8, 2, 1, 8, 7, 6, 5, 4, 3, 2, 1, 0, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 5, 8, 8, 2, 1, 8, 4, 0, 8, 8, 3, 2, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 7, 6, 5, 4, 3, 2, 1, 0, 8, 8, 8, 8, 8, 8, 1, 8, 8, 8, 5, 8, 8, 2, 8, 8, 8, 8, 8, 4, 8, 2, 8, 8, 4, 0, 8, 8, 3, 2, 1, 8, 8

Offset

1,1

Links

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

Mathematica

p = 8; 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], Which[n == 49, z = 4; fz = $Aborted, n == 81, z = 8; fz = $Aborted, n == 83, z = 5; fz = $Aborted, n == 101, z = 3; fz = $Aborted, True, 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: A377636 A019906 A197251 * A175621 A016578 A268631

Adjacent sequences: A049244 A049245 A049246 * A049248 A049249 A049250

Keyword

nonn

Author

David W. Wilson

Status

approved