OFFSET
0,1
COMMENTS
The arithmetic mean 1/(n+1)*sum(a(k)|k=0...n) converges to Pi-3. What is effectively the same: the Cesaro limit (C1) of a(n) is Pi-3.
FORMULA
a(n) = 1 - (Floor((n+1)*Pi)-Floor(n*Pi)) mod 2.
a(n) = 1 - A115789(n). - Michel Marcus, Jul 15 2013
EXAMPLE
a(6)=0 because 7*Pi=21.99, 6*pi=18.85 and so a(6)=1-(21-18) mod 2 = 0;
a(7)=1 because 8*Pi=25.13 and so a(7)=1-(25-21) mod 2 = 1;
MATHEMATICA
Mod[1-(Last[#]-First[#]), 2]&/@(Partition[Floor[Pi #]&/@ Range[ 0, 110], 2, 1]) (* Harvey P. Dale, Oct 12 2012 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Hieronymus Fischer, Jan 31 2006
STATUS
approved