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%I #8 Oct 11 2016 08:06:37
%S 4,0,5,4,3,2,1,0,8,8,8,8,8,2,8,8,4,0,8,8,8,2,1,8,7,6,5,4,3,2,1,0,8,8,
%T 8,8,8,2,8,8,8,8,5,8,8,2,1,8,4,0,8,8,3,2,8,8,8,8,8,8,8,2,8,8,7,6,5,4,
%U 3,2,1,0,8,8,8,8,8,8,1,8,8,8,5,8,8,2,8,8,8,8,8,4,8,2,8,8,4,0,8,8,3,2,1,8,8
%N Smallest nonnegative value taken on by 8x^2 - ny^2 for an infinite number of integer pairs (x, y).
%t p = 8; 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 == 49, z = 4; fz = $Aborted, n == 81, z = 8; fz = $Aborted, n == 83, z = 5; fz = $Aborted, n == 101, z = 3; 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, 105}] (* _Jean-François Alcover_, Oct 11 2016 *)
%K nonn
%O 1,1
%A _David W. Wilson_
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