A373304 -id:A373304 - cp's OEIS frontend

A373079 Decimal digits of Pi selected by stepping forward d places at digit d or 10 places if d=0.

3, 1, 5, 3, 9, 2, 4, 3, 9, 7, 3, 1, 0, 4, 3, 8, 6, 8, 2, 3, 1, 1, 7, 1, 4, 6, 2, 0, 4, 5, 2, 3, 2, 3, 4, 2, 4, 1, 7, 1, 0, 1, 1, 0, 2, 4, 4, 3, 9, 9, 4, 2, 4, 4, 3, 6, 5, 0, 8, 6, 1, 0, 2, 3, 3, 7, 1, 4, 3, 4, 0, 8, 5, 0, 0, 6, 9, 3, 3, 4, 0, 1, 4, 1, 9, 4, 5, 3, 7, 5, 1, 8, 9, 1, 0, 4, 3, 9, 3, 8

Offset: 1

Karl Levy, May 22 2024

Are the digits uniformly distributed?

			The sequence starts with the first digit of the decimal expansion of Pi, which is 3. The next term is the digit 3 places after this, namely, 1, and so on.
The digits selected from Pi begin
  Pi = 3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8, 9, ...
       ^        ^  ^              ^        ^

Cf. A000796,

Cf. A373304, A373307.

a={3}; s=1; For[n=2, n<=100, n++, s+=Part[a,n-1]+10KroneckerDelta[Part[a,n-1]]; digits=First[RealDigits[Pi,10,s]]; AppendTo[a,Part[digits,s]]]; a (* Stefano Spezia, May 31 2024 *)

a(n) = the (1 + Sum_{i=1..n-1} a(i) + 10*delta(a(i),0))-th digit in the decimal expansion of Pi, where delta is the Kronecker symbol.

a(25)-a(100) from Stefano Spezia, May 31 2024

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

Original entry on oeis.org

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

Karl Levy, May 31 2024

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

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

Cf. A004601.

Cf. A373079, A373304.

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

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

cp's OEIS Frontend

A373079 Decimal digits of Pi selected by stepping forward d places at digit d or 10 places if d=0.

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