A049263 - OEIS

A049263

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

0, 2, 3, 0, 1, 2, 3, 4, 0, 4, 7, 8, 1, 10, 11, 0, 1, 2, 3, 4, 5, 2, 7, 8, 0, 4, 8, 12, 1, 14, 3, 16, 17, 18, 19, 0, 1, 2, 3, 4, 1, 6, 3, 8, 5, 10, 11, 12, 0, 4, 8, 4, 1, 2, 11, 20, 12, 4, 8, 24, 1, 26, 27, 0, 1, 2, 3, 4, 5, 6, 7, 8, 1, 4, 11, 8, 13, 14, 15, 16, 0, 4, 8, 12, 1, 2, 23, 8, 1, 26, 3

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..91.

MATHEMATICA

p = 4; f[n_, z_] := FindInstance[x > 0 && y > 0 && n*x^2 - p*y^2 == z, {x, y}, Integers, 1]; a[n_] := For[z = 0, True, z = z + GCD[n, p], fz = TimeConstrained[f[n, z], 300]; fz = If[fz === $Aborted, {{x -> Null, y -> Null}}, fz]; If[fz =!= {}, Print["a(", n, ") = ", z, " {x, y} = ", {x, y} /. fz[[1]]]; Return[z]]]; Table[a[n], {n, 1, 91}] (* Jean-François Alcover, Oct 11 2016 *)

CROSSREFS

Sequence in context: A309954 A124757 A242305 * A014588 A293497 A278164

Adjacent sequences: A049260 A049261 A049262 * A049264 A049265 A049266

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved