

A120749


Numbers k such that {k* sqrt(2)} > 1/2, where { } = fractional part.


6



2, 4, 7, 9, 11, 12, 14, 16, 19, 21, 23, 24, 26, 28, 31, 33, 36, 38, 40, 41, 43, 45, 48, 50, 52, 53, 55, 57, 60, 62, 64, 65, 67, 69, 70, 72, 74, 77, 79, 81, 82, 84, 86, 89, 91, 93, 94, 96, 98, 101, 103, 106, 108, 110, 111, 113, 115, 118, 120, 122, 123, 125, 127, 130, 132, 134
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS



LINKS



EXAMPLE

Call the present sequence b and its complement a. Then
{r} = {1.4142...} = 0.4142... < 1/2, so a(1) = 1;
{2r} = 0.828... > 1/2, so b(1) = 2;
{3r} = 0.242... < 1/2, so a(2) = 3.


MATHEMATICA

z = 150; r = Sqrt[2]; f[n_] := If[FractionalPart[n*r] < 1/2, 0, 1]
Flatten[Position[Table[f[n], {n, 1, z}], 0]] (* A120243 *)
Flatten[Position[Table[f[n], {n, 1, z}], 1]] (* A120749 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



