A182101 Random walk determined by the binary digits of the Dottie number, A003957.

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, 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, 9, 10, 9, 10

Offset: 0

Author

Ben Branman, Apr 11 2012

Keywords

• sign
• base

Comments

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.

Partial sums of the sequence 2*A121967(n)-1.

The first time a(n) is negative is n=93.

Examples

			a(5)=3, and the sixth bit of the Dottie number is 1, so a(6)=4.
On the other hand, the seventh bit of the Dottie number is 0, so a(7)=3.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000

Crossrefs

Cf. A003957, A121967, A166006 (analogous sequence for Pi).

Programs

Mathematica

Accumulate[RealDigits[FindRoot[Cos[x] == x, {x, 0}, WorkingPrecision -> 1000][[1, -1]], 2][[1]] 2 - 1]