A049251 Smallest nonnegative value taken on by 12x^2 - ny^2 for an infinite number of integer pairs (x, y).

3, 4, 0, 8, 3, 6, 5, 4, 3, 2, 1, 0, 12, 12, 12, 12, 3, 12, 12, 12, 3, 12, 1, 12, 3, 4, 0, 12, 3, 12, 12, 12, 3, 12, 12, 12, 11, 10, 9, 8, 3, 6, 5, 4, 3, 2, 1, 0, 12, 12, 12, 12, 3, 12, 5, 12, 3, 2, 1, 12, 12, 12, 12, 12, 3, 12, 5, 12, 3, 12, 1, 12, 3, 4, 0, 12, 3, 12, 12, 12, 3, 12, 1, 12

Offset

1,1

Links

Table of n, a(n) for n=1..84.

Mathematica

p = 12; 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], 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, 84}] (* Jean-François Alcover, Oct 11 2016 *)

Crossrefs

Sequence in context: A011338 A214024 A215079 * A308642 A158674 A077628

Adjacent sequences: A049248 A049249 A049250 * A049252 A049253 A049254

Keyword

nonn

Author

David W. Wilson, Dec 11 1999

Status

approved