%I
%S 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,
%T 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,
%U 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
%N Smallest nonnegative value taken on by 12x^2  ny^2 for an infinite number of integer pairs (x, y).
%t 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}] (* _JeanFrançois Alcover_, Oct 11 2016 *)
%K nonn
%O 1,1
%A _David W. Wilson_, Dec 11 1999
