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%I #7 Oct 11 2016 11:04:34
%S 1,2,7,4,5,4,3,2,1,0,10,10,3,10,10,10,7,10,10,10,6,2,10,10,10,10,7,10,
%T 10,10,1,8,7,6,5,4,3,2,1,0,10,10,10,10,10,10,10,10,6,10,10,10,10,4,10,
%U 10,10,10,10,10,6,2,10,10,10,6,10,10,10,10,1,10,10,10,10,10,10,10,1,10
%N Smallest nonnegative value taken on by 10x^2 - ny^2 for an infinite number of integer pairs (x, y).
%t p = 10; 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 == 64, z = 10; 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, 80}] (* _Jean-François Alcover_, Oct 11 2016 *)
%K nonn
%O 1,2
%A _David W. Wilson_
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