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A120243 Numbers k such that {k*sqrt(2)} < 1/2, where { } = fractional part. 8
1, 3, 5, 6, 8, 10, 13, 15, 17, 18, 20, 22, 25, 27, 29, 30, 32, 34, 35, 37, 39, 42, 44, 46, 47, 49, 51, 54, 56, 58, 59, 61, 63, 66, 68, 71, 73, 75, 76, 78, 80, 83, 85, 87, 88, 90, 92, 95, 97, 99, 100, 102, 104, 105, 107, 109, 112, 114, 116, 117, 119, 121, 124, 126, 128, 129 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The complement of a is b=A120749. Is a(n) < b(n) for all n? If k is a positive integer, then is b(n) - a(n) = k for infinitely many n?

LINKS

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

EXAMPLE

{r} = {1.4142...} = 0.4142... < 1/2, so a(1)=1.

{2r} = 0.828... > 1/2, so b(1) = 2, where b = complement of a.

{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

Cf. A120749, A120750, A120751.

Sequence in context: A024705 A190192 A187977 * A304435 A084810 A268896

Adjacent sequences:  A120240 A120241 A120242 * A120244 A120245 A120246

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jul 01 2006

EXTENSIONS

Updated by Clark Kimberling, Sep 16 2014

STATUS

approved

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Last modified May 13 13:53 EDT 2021. Contains 343858 sequences. (Running on oeis4.)