A049250 Smallest nonnegative value taken on by 11x^2 - ny^2 for an infinite number of integer pairs (x, y).

2, 1, 8, 7, 6, 3, 1, 3, 2, 1, 0, 11, 11, 2, 11, 11, 3, 9, 1, 11, 11, 11, 7, 3, 11, 2, 8, 4, 3, 5, 11, 3, 11, 10, 1, 8, 7, 6, 5, 4, 3, 2, 1, 0, 11, 11, 11, 11, 2, 1, 3, 11, 6, 5, 11, 8, 11, 2, 8, 11, 11, 3, 9, 11, 11, 11, 7, 3, 11, 11, 11, 11, 11, 1, 11, 4, 11, 2, 1, 11, 2, 11, 1, 11, 11, 6

Offset

1,1

Links

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

Mathematica

p = 11; 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 == 64, z = 11; 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, 86}] (* Jean-François Alcover, Oct 11 2016 *)

Crossrefs

Sequence in context: A293415 A197018 A082532 * A060587 A168142 A081800

Adjacent sequences: A049247 A049248 A049249 * A049251 A049252 A049253

Keyword

nonn

Author

David W. Wilson, Dec 11 1999

Status

approved