A115788 a(n) = floor(n*Pi) mod 2.

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

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 A351077 A229940

Adjacent sequences: A115785 A115786 A115787 * A115789 A115790 A115791

Keyword

nonn

Author

Hieronymus Fischer, Jan 31 2006

Status

approved