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A049261 Smallest nonnegative value taken on by nx^2 - 2y^2 for an infinite number of integer pairs (x, y). 0

%I

%S 1,0,1,2,2,4,5,0,1,2,1,4,2,6,7,8,9,0,1,2,3,4,5,6,2,2,1,10,2,12,13,0,1,

%T 2,3,4,2,4,7,8,2,6,1,4,13,14,5,16,17,0,1,2,2,4,5,6,1,2,1,10,2,6,7,14,

%U 2,16,1,18,19,20,21,0,1,2,3,4,3,6,7,8,1,2,1,12,2,4,10,14,1,10,19,10,3,22

%N Smallest nonnegative value taken on by nx^2 - 2y^2 for an infinite number of integer pairs (x, y).

%t p = 2; 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, 94}] (* _Jean-Fran├žois Alcover_, Oct 11 2016 *)

%K nonn

%O 1,4

%A _David W. Wilson_, Dec 11 1999

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Last modified July 2 12:39 EDT 2022. Contains 355004 sequences. (Running on oeis4.)