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A049262 Smallest nonnegative value taken on by nx^2 - 3y^2 for an infinite number of integer pairs (x, y). 0

%I

%S 1,2,0,1,2,3,1,5,6,7,8,0,1,2,3,4,5,6,1,5,9,6,5,12,13,14,0,1,2,3,1,5,6,

%T 6,8,9,1,5,3,13,6,15,1,17,18,19,20,0,1,2,3,4,2,6,7,8,6,10,8,12,1,2,9,

%U 13,17,6,1,5,21,22,11,24,25,26,0,1,2,3,1,5,6,6,5,9,10,6,3,13,6,15,1,5

%N Smallest nonnegative value taken on by nx^2 - 3y^2 for an infinite number of integer pairs (x, y).

%t p = 3; 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, 92}] (* _Jean-Fran├žois Alcover_, Oct 11 2016 *)

%K nonn

%O 1,2

%A _David W. Wilson_, Dec 11 1999

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Last modified August 14 03:14 EDT 2022. Contains 356109 sequences. (Running on oeis4.)