A115790 a(n) = 1 - (floor((n+1)*Pi) - floor(n*Pi)) mod 2.

0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0

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.

Links

Table of n, a(n) for n=0..104.

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

Cf. A000796, A022844, A063438, A115788, A115789.

Sequence in context: A188436 A037823 A293162 * A025460 A374222 A169673

Adjacent sequences: A115787 A115788 A115789 * A115791 A115792 A115793

Keyword

nonn

Author

Hieronymus Fischer, Jan 31 2006

Status

approved