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
Paolo Xausa, Table of n, a(n) for n = 1..10000
Peter Borwein and Loki Jörgenson, Visible Structures in Number Theory, The American Mathematical Monthly, Vol. 108, 2001, No. 10, pp. 906-908.
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
KEYWORD
nonn
AUTHOR
Hieronymus Fischer, Jan 31 2006
STATUS
approved