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

0,5

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.

Links

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

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A106826 A259582 A139048 * A242289 A349229 A158515

Adjacent sequences: A182098 A182099 A182100 * A182102 A182103 A182104

Keyword

sign,base

Author

Ben Branman, Apr 11 2012

Status

approved