|
%I #8 Oct 11 2016 05:31:17
%S 3,5,1,3,2,1,0,7,7,2,7,4,2,7,3,7,7,7,1,7,7,6,5,4,3,2,1,0,7,7,1,7,7,7,
%T 7,7,3,1,7,7,7,7,3,7,7,7,1,7,7,7,3,7,7,1,7,7,6,5,1,3,2,1,0,7,7,7,7,7,
%U 7,7,7,7,7,7,7,4,7,7,3,7,7,7,1,7,3,7,1,7,7,7,7,7,7,1,5,7,7,7,7,3,2,6,1,7,7
%N Smallest nonnegative value taken on by 7x^2 - ny^2 for an infinite number of integer pairs (x, y).
%t p = 7; 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], Switch[n, 64 | 81, z = p; fz = $Aborted, _, 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 *)
%K nonn
%O 1,1
%A _David W. Wilson_
|
