A049244 Smallest nonnegative value taken on by 5x^2 - ny^2 for an infinite number of integer pairs (x, y).

1, 2, 2, 1, 0, 5, 5, 5, 5, 5, 1, 5, 5, 5, 5, 4, 3, 2, 1, 0, 5, 5, 5, 5, 5, 5, 2, 5, 5, 5, 1, 5, 3, 5, 5, 5, 5, 5, 5, 5, 1, 3, 2, 1, 0, 5, 5, 5, 5, 5, 5, 5, 3, 5, 5, 5, 5, 5, 1, 5, 1, 2, 5, 5, 5, 5, 2, 5, 5, 5, 1, 5, 5, 5, 5, 4, 3, 2, 1, 0, 5, 5, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3, 5, 5, 1, 5, 5, 5, 5

Offset

1,2

Links

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

Mathematica

f[n_, z_] := FindInstance[x > 0 && y > 0 && 5*x^2 - n*y^2 == z, {x, y}, Integers, 1]; a[n_] := For[z = 0, z <= 5, z = z + GCD[n, 5], 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} = ", {51841, 16560}]; 5);
a[81] := (Print["a(81) = ", 5, " {x, y} = ", {161, 40}]; 5);
a[83] := (Print["a(83) = ", 5, " {x, y} = ", {1919, 471}]; 5);
a[98] := (Print["a(98) = ", 3, " {x, y} = ", {31, 7}]; 3);
Table[TimeConstrained[a[n], 300], {n, 1, 105}] (* Jean-François Alcover, Oct 10 2016 *)

Crossrefs

Sequence in context: A106566 A099039 A205574 * A110281 A120059 A067347

Adjacent sequences: A049241 A049242 A049243 * A049245 A049246 A049247

Keyword

nonn

Author

David W. Wilson

Status

approved