%I
%S 0,1,0,1,2,3,4,3,4,3,2,3,4,3,4,3,2,3,2,3,2,3,4,5,4,5,6,7,6,7,8,7,6,5,
%T 4,3,4,5,6,7,6,5,6,7,8,7,6,5,6,5,6,7,6,7,8,7,8,9,10,9,8,9,8,9,8,9,10,
%U 9,10,9,10
%N Random walk determined by the binary digits of the Dottie number, A003957.
%C Start at a(0)=0. Each 0 in the binary expansion corresponds to a step of 1, while a 1 corresponds to a step of +1.
%C Partial sums of the sequence 2*A121967(n)1.
%C The first time a(n) is negative is n=93.
%H G. C. Greubel, <a href="/A182101/b182101.txt">Table of n, a(n) for n = 0..5000</a>
%e a(5)=3, and the sixth bit of the Dottie number is 1, so a(6)=4.
%e On the other hand, the seventh bit of the Dottie number is 0, so a(7)=3.
%t Accumulate[RealDigits[FindRoot[Cos[x] == x, {x, 0}, WorkingPrecision > 1000][[1, 1]], 2][[1]] 2  1]
%Y Cf. A003957, A121967, A166006 (analogous sequence for Pi).
%K sign,base
%O 0,5
%A _Ben Branman_, Apr 11 2012
