login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A115788 a(n) = floor(n*Pi) mod 2. 4
1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

The arithmetic mean (1/(n+1))*Sum_{k=0...n} a(k) converges to 1/2. What is effectively the same: the Cesaro limit (C1) of a(n) is 1/2. When we pick a term of the sequence at random, the probability of getting a '1' is 1/2. If we select a '1' randomly, the probability p11 of finding a '1' as the next term right of it is p11 = Pi - 3. If we select a '1' randomly, the probability p10 of finding a '0' as the next term right of it is p10 = 4 - Pi. Analogous statements hold for '0' --> '0' (p00 = p11) and '0' --> '1' (p01 = p10).

First differs from A195062 at a(113). - Alois P. Heinz, Jan 22 2012

LINKS

Table of n, a(n) for n=1..150.

FORMULA

a(n) = floor(n*Pi) mod 2.

EXAMPLE

a(2) = 0 because floor(2*Pi) = floor(6.28... ) = 6,

a(8) = 1 because floor(8*Pi) = floor(25.13...) = 25.

MAPLE

a:= proc(n) Digits:= length(n) +15; floor(n*Pi) mod 2 end:

seq(a(n), n=1..150);  # Alois P. Heinz, Jan 22 2012

MATHEMATICA

Floor[Mod[\[Pi] Range[110], 2]]  (* Harvey P. Dale, Apr 02 2011 *)

CROSSREFS

Cf. A022844, A063438, A115789, A115790.

Cf. A195062. - Alois P. Heinz, Jan 22 2012

Sequence in context: A285592 A276793 A284364 * A195062 A229940 A179761

Adjacent sequences:  A115785 A115786 A115787 * A115789 A115790 A115791

KEYWORD

nonn

AUTHOR

Hieronymus Fischer, Jan 31 2006

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 23 01:55 EDT 2021. Contains 343198 sequences. (Running on oeis4.)