0,1

The arithmetic mean 1/(n+1)*sum(a(k)|k=0...n) 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 by random, the probability to get a '1' is 1/2. If we select a '1' randomly, the probability p11 to find a '1' as the next term right of it is p11=pi-3. If we select a '1' randomly, the probability p10 to find 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).

a(n) = Floor(n*pi) mod 2.

a(2)=0 because Floor(2*pi)=Floor(6.28...)=6;

a(8)=1 because Floor(8*pi)=Floor(25.13...)=25;

Cf. A022844, A115787, A115789, A115790.

Sequence in context: A071022 A071025 A162549 this_sequence A102863 A131483 A077052

Adjacent sequences: A115785 A115786 A115787 this_sequence A115789 A115790 A115791

nonn

Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jan 31 2006