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A049242 Smallest nonnegative value taken on by 3x^2 - ny^2 for an infinite number of integer pairs (x, y). 0

%I #9 Oct 10 2016 02:45:31

%S 2,1,0,3,3,3,3,3,3,2,1,0,3,3,3,3,3,3,3,3,3,3,1,3,2,1,0,3,3,3,3,3,3,3,

%T 3,3,3,3,3,3,3,3,3,3,3,2,1,0,3,3,3,3,3,3,3,3,3,2,1,3,3,3,3,3,3,3,3,3,

%U 3,3,1,3,2,1,0,3,3,3,3,3,3,3,1,3,3,3,3,3,3,3,3,3,3,2,3,3,3,3,3,3,3,3,3,3,3

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

%t f[n_, z_] := FindInstance[x > 0 && y > 0 && 3*x^2 - n*y^2 == z, {x, y}, Integers,1]; a[n_] := For[z = 0, True, z = z + GCD[n, 3], fz = f[n, z]; If[fz =!= {}, Print["a(", n, ") = ", z, " {x,y} = ", {x, y} /. fz[[1]]]; Return[z]]]; a[32] := (Print["a(32) = ", 3, " {x,y} = ", {4801, 1470}]; 3); a[64] := (Print["a(64) = ", 3, " {x,y} = ", {97, 21}]; 3); a[101] := (Print["a(101) = ", 3, " {x,y} = ", {2524, 435}]; 3); a[103] := (Print["a(103) = ", 3, " {x,y} = ", {64202725495, 10957096332}]; 3); Table[TimeConstrained[a[n], 300], {n, 1, 105}] (* _Jean-Fran├žois Alcover_, Oct 09 2016 *)

%K nonn

%O 1,1

%A _David W. Wilson_

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Last modified July 12 07:24 EDT 2024. Contains 374237 sequences. (Running on oeis4.)