A115789 a(n) = (floor((n+1)*Pi) - floor(n*Pi)) mod 2.

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

Offset

0,1

Comments

The arithmetic mean (1/(n+1))*Sum_{k=0..n} a(k) converges to 4 - Pi. What is effectively the same: the Cesaro limit (C1) of a(n) is 4 - Pi.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..10000

Formula

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

a(n) = A063438(n) mod 2.

a(n) = 1 - A115790(n).

Example

a(6)=1 because 7*Pi=21.99..., 6*Pi=18.84... and so a(6) = (21 - 18) mod 2 = 1;
a(7)=0 because 8*Pi=25.13... and so a(7) = (25 - 21) mod 2 = 0.

Mathematica

Mod[Differences[Floor[Pi*Range[0, 120]]], 2] (* Paolo Xausa, Nov 07 2025 *)

Crossrefs

Cf. A000796, A022844, A063438, A115788, A115790.

Sequence in context: A118111 A305940 A119981 * A359471 A363551 A053864

Adjacent sequences: A115786 A115787 A115788 * A115790 A115791 A115792

Keyword

nonn,less

Author

Hieronymus Fischer, Jan 31 2006

Status

approved