A049243 Smallest nonnegative value taken on by 4x^2 - ny^2 for an infinite number of integer pairs (x, y).

0, 2, 1, 0, 4, 4, 1, 4, 0, 4, 1, 4, 3, 2, 1, 0, 4, 4, 1, 4, 4, 4, 1, 4, 0, 4, 1, 4, 4, 4, 1, 4, 3, 2, 1, 0, 4, 4, 4, 4, 4, 4, 1, 4, 4, 2, 1, 4, 0, 4, 1, 4, 4, 4, 4, 4, 4, 4, 1, 4, 3, 2, 1, 0, 4, 4, 1, 4, 3, 4, 1, 4, 3, 4, 1, 4, 4, 4, 1, 4, 0, 4, 1, 4, 4, 4, 1, 4, 4, 4, 1, 4, 4, 2, 4, 4, 3, 2, 1, 0, 4, 4, 1, 4, 4

Offset

1,2

Links

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

Mathematica

f[n_, z_] := FindInstance[x > 0 && y > 0 && 4*x^2 - n*y^2 == z, {x, y}, Integers, 1]; a[n_] := For[z = 0, z <= 4, z = z + GCD[n, 4], fz = f[n, z]; If[fz =!= {}, Print["a(", n, ") = ", z, " {x, y} = ", {x, y} /. fz[[1]]]; Return[z]]]; a[89] := (Print["a(89) = ", 4, " {x, y} = ", {500001, 106000}]; 4); a[97] := (Print["a(97) = ", 3, " {x, y} = ", {5, 1}]; 3); Table[TimeConstrained[a[n], 300], {n, 1, 105}] (* Jean-François Alcover, Oct 09 2016 *)

Crossrefs

Sequence in context: A276544 A214753 A158454 * A077908 A052922 A181930

Adjacent sequences: A049240 A049241 A049242 * A049244 A049245 A049246

Keyword

nonn

Author

David W. Wilson

Status

approved