

A049243


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


0



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
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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}] (* JeanFrançois 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



