A049248 Smallest nonnegative value taken on by 9x^2 - ny^2 for an infinite number of integer pairs (x, y).

0, 1, 6, 0, 1, 3, 2, 1, 0, 9, 9, 9, 9, 1, 9, 0, 1, 9, 5, 1, 9, 9, 1, 9, 0, 1, 9, 8, 1, 6, 2, 4, 3, 2, 1, 0, 9, 9, 9, 9, 1, 9, 9, 9, 9, 2, 1, 9, 0, 1, 9, 9, 1, 9, 5, 1, 9, 9, 9, 9, 5, 1, 9, 0, 1, 9, 9, 1, 3, 9, 1, 9, 8, 1, 6, 5, 1, 3, 2, 1, 0, 9, 9, 9, 9, 9, 9, 9, 1, 9, 9, 4, 9, 2, 1, 9, 8, 1, 9, 0, 1, 9, 2, 1, 9

Offset

1,3

Links

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

Mathematica

p = 9; 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 == 97, z = 8; fz = $Aborted, n == 103, z = 2; 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: A063085 A020796 A011253 * A178601 A094691 A095715

Adjacent sequences: A049245 A049246 A049247 * A049249 A049250 A049251

Keyword

nonn

Author

David W. Wilson

Status

approved