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

Author

Karl Levy, May 31 2024

Keywords

• nonn
• base

Comments

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

Examples

			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, ...
     ^     ^  ^  ^     ^  ^     ^  ^  ^  ^     ^
		

Crossrefs

Cf. A004601.

Cf. A373079, A373304.

Programs

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

Formula

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