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%I #8 Oct 11 2016 20:08:11
%S 0,2,3,0,1,2,3,4,0,4,7,8,1,10,11,0,1,2,3,4,5,2,7,8,0,4,8,12,1,14,3,16,
%T 17,18,19,0,1,2,3,4,1,6,3,8,5,10,11,12,0,4,8,4,1,2,11,20,12,4,8,24,1,
%U 26,27,0,1,2,3,4,5,6,7,8,1,4,11,8,13,14,15,16,0,4,8,12,1,2,23,8,1,26,3
%N Smallest nonnegative value taken on by n*x^2 - 4*y^2 for an infinite number of integer pairs (x, y).
%t p = 4; 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, 91}] (* _Jean-François Alcover_, Oct 11 2016 *)
%K nonn
%O 1,2
%A _David W. Wilson_
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