A199693 Related to the expansion of Pi in base 2 (A004601).

12, 4, 16, 126, 6, 2, 2, 8, 8, 16, 2, 6, 8, 48, 8, 6, 4, 24, 4, 24, 12, 24, 2, 8, 2, 896, 6, 224, 28, 6, 8, 4, 2, 4, 64, 4, 4, 224, 8, 8, 2, 4, 12, 124, 24, 14, 256, 32, 2, 14, 62, 2, 4, 24, 14, 24, 4, 28, 6, 12, 8, 4, 2, 8, 2, 4, 2, 32, 16, 60, 24, 56, 6

Offset

1,1

Comments

A004601 is the concatenation of binary digits of the terms written in base 2.

Links

Table of n, a(n) for n=1..73.

Example

A004601( expansion of Pi in base 2) :
1,1,0,0,1,0,0,1,0,0,0,0,1,1,1,1,1,1,0,1,1,0,1,0,1,0.... ->
1,1,0,0 | 1,0,0 | 1,0,0,0,0 | 1,1,1,1,1,1,0 | 1,1,0 | 1,0 | ... ->
1100 | 100 |10000 | 1111110 |110 |10 | 10 | ... (in base 2) ->
12 , 4, 16, 126, 6, 2, 2, ... (in base 10) .

Mathematica

f[{a_, b_}] := (2^a - 1)*2^b; f /@ Partition[Length /@ Split[First[RealDigits[π, 2, 10^3]]], 2] (* T. D. Noe, Nov 09 2011 *)

Prog

(Python)
import gmpy2
pi = gmpy2.const_pi(precision=310) # increase precision for more terms
h = "{0:A}".format(pi)[2:-5].replace(".", "")
b = bin(int(h, 16))[2:]
splitb = b.replace("01", "0, 1").split(", ")
print([int(t, 2) for t in splitb[:-1]]) # Michael S. Branicky, Dec 04 2021

Crossrefs

Cf. A004601, A007088.

Sequence in context: A307164 A181829 A339467 * A166206 A040137 A092237

Adjacent sequences: A199690 A199691 A199692 * A199694 A199695 A199696

Keyword

easy,nonn,base

Author

Philippe Deléham, Nov 09 2011

Status

approved