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

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, 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, 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

Offset

1,1

Links

Table of n, a(n) for n=1..105.

Mathematica

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 *)

Crossrefs

Sequence in context: A341606 A109158 A307500 * A123547 A123551 A286275

Adjacent sequences: A049242 A049243 A049244 * A049246 A049247 A049248

Keyword

nonn

Author

David W. Wilson

Status

approved