A120749 Numbers k such that {k* sqrt(2)} > 1/2, where { } = fractional part.

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

Offset

1,1

Comments

The complement of A120749 is A120243.

Links

Clark Kimberling, Table of n, a(n) for n = 1..1000

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 *)
Select[Range[200], FractionalPart[# Sqrt[2]]>1/2&] (* Harvey P. Dale, Aug 20 2024 *)

Crossrefs

Cf. A120243, A120750, A120751.

Sequence in context: A226812 A185978 A351799 * A187978 A190193 A353737

Adjacent sequences: A120746 A120747 A120748 * A120750 A120751 A120752

Keyword

nonn

Author

Clark Kimberling, Jul 01 2006

Extensions

Updated by Clark Kimberling, Sep 16 2014

Status

approved