A373307 - OEIS

%I #19 Jun 28 2024 23:09:14

%S 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,

%T 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,

%U 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

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

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

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

%e 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.

%e The digits selected from Pi begin

%e   Pi=1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, ...

%e      ^     ^  ^  ^     ^  ^     ^  ^  ^  ^     ^

%t 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

%Y Cf. A004601.

%Y Cf. A373079, A373304.

%K nonn,base

%O 1,1

%A _Karl Levy_, May 31 2024