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

Author

Hieronymus Fischer, Jan 31 2006

Keywords

• nonn

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.

Examples

			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;
		

Crossrefs

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

Programs

Mathematica

Mod[1-(Last[#]-First[#]),2]&/@(Partition[Floor[Pi #]&/@ Range[ 0,110],2,1]) (* Harvey P. Dale, Oct 12 2012 *)

Formula

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

a(n) = 1 - A115789(n). - Michel Marcus, Jul 15 2013