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 A049245 Smallest nonnegative value taken on by 6x^2 - ny^2 for an infinite number of integer pairs (x, y). 0

%I #9 Oct 10 2016 06:46:47

%S 2,4,3,2,1,0,6,6,6,6,6,6,2,6,6,6,6,6,5,4,3,2,1,0,6,6,6,6,1,6,6,6,6,6,

%T 6,6,2,6,6,6,6,6,6,6,6,2,1,6,5,4,3,2,1,0,6,6,6,6,6,6,2,6,6,6,6,6,6,6,

%U 3,6,1,6,2,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,5,4,3,2,1,0,6,6,6,6,1,6,6,6,6

%N Smallest nonnegative value taken on by 6x^2 - ny^2 for an infinite number of integer pairs (x, y).

%t f[n_, z_] := FindInstance[x > 0 && y > 0 && 6*x^2 - n*y^2 == z, {x, y}, Integers, 1]; a[n_] := For[z = 0, z <= 6, z = z + GCD[n, 6], fz = f[n, z]; If[fz =!= {}, Print["a(", n, ") = ", z, " {x, y} = ", {x, y} /. fz[[1]]]; Return[z]]]; a[49] := (Print["a(49) = ", 5, " {x, y} = ", {3, 1}]; 5); a[64] := (Print["a(64) = ", 6, " {x, y} = ", {49, 15}]; 6); a[101] := (Print["a(101) = ", 1, " {x, y} = ", {1875, 457}]; 1); Table[TimeConstrained[a[n], 300], {n, 1, 105}] (* _Jean-François Alcover_, Oct 10 2016 *)

%K nonn

%O 1,1

%A _David W. Wilson_

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Last modified August 5 14:51 EDT 2024. Contains 374950 sequences. (Running on oeis4.)