%I
%S 1,2,3,4,5,0,1,2,3,4,3,6,7,2,6,10,3,12,3,14,15,16,17,0,1,2,3,4,5,6,1,
%T 8,3,10,11,12,13,2,6,10,3,18,3,12,21,10,23,24,1,26,27,28,29,0,1,2,3,4,
%U 3,6,7,2,9,10,11,12,3,12,15,16,17,18,19,2,6,10,14,6,1,26,3,12,3,30,10,2
%N Smallest nonnegative value taken on by n*x^2  6*y^2 for an infinite number of integer pairs (x, y).
%t p = 6; f[n_, z_] := FindInstance[x > 0 && y > 0 && n*x^2  p*y^2 == z, {x, y}, Integers, 1]; a[n_] := For[z = 0, True, 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, 86}] (* _JeanFrançois Alcover_, Oct 11 2016 *)
%K nonn
%O 1,2
%A _David W. Wilson_, Dec 11 1999
