A373307 Binary digits of Pi selected by stepping forward d+1 places at digit d, i.e., by skipping the next d places.

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

Offset

1,1

Comments

Are the digits uniformly distributed? Are all digit sequences uniformly distributed?

Links

Table of n, a(n) for n=1..100.

Formula

a(n) = the (n+a(1)+a(2)+...+a(n-1))-th digit in the binary expansion of Pi.

Example

The sequence starts with the first digit of the binary expansion of Pi, which is 1. The next term is the digit 1+1 places after this, namely, 0, and so on.
The digits selected from Pi begin
  Pi=1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, ...
     ^     ^  ^  ^     ^  ^     ^  ^  ^  ^     ^

Mathematica

a={1}; s=1; For[n=2, n<=100, n++, s+=Part[a, n-1]+1; digits=First[RealDigits[Pi, 2, s]]; AppendTo[a, Part[digits, s]]]; a

Crossrefs

Cf. A004601.

Cf. A373079, A373304.

Sequence in context: A352569 A101266 A260552 * A244612 A262805 A213728

Adjacent sequences: A373304 A373305 A373306 * A373308 A373309 A373310

Keyword

nonn,base

Author

Karl Levy, May 31 2024

Status

approved