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A004601 Expansion of Pi in base 2 (or, binary expansion of Pi). 51
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, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

The 10^k_th binary digit of Pi beginning with k=0: 0,0,0,1,1,0,1,1,0, ..., . - Robert G. Wilson v, May 04 2009

It appears to me that, if this is read as a decimal number, it is an example of an irrational number that is not normal (no '2' for example, and if it repeated or terminated, pi would too). - Alvin H. Belt, Jun 19 2009

REFERENCES

J. P. Delahaye, Le Fascinant Nombre Pi, "100000 digits of pi in base two", pp. 209-210; Pour la Science, Paris 1997.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 2..1000

Francisco Javier Aragón Artacho, 2 billion step walk on the digits of pi

A. Brouty, Les decimales de PI en base 2 jusqu'a 1 million

Elias's Pi Page, Binary representation of pi with 32768 digits

J. Leroy, M. Rigo, and M. Stipulanti, Behavior of Digital Sequences Through Exotic Numeration Systems, Electronic Journal of Combinatorics 24(1) (2017), #P1.44. See w(n) in Example 19.

Steve Pagliarulo, Stu's pi page: base 2 (23 pages)

FORMULA

a(n) = -2*floor(Pi*2^(-4 + n)) + floor(Pi*2^(-3 + n)) for n > 1. - Mariusz Iwaniuk, Apr 28 2017

EXAMPLE

11.0010010000111111011010101000100010000...

MATHEMATICA

RealDigits[Pi, 2, 75][[1]]

Table[-2 Floor[Pi 2^(-4 + n)] + Floor[Pi 2^(-3 + n)], {n, 2, 100}] (* Vincenzo Librandi, Apr 30 2017 *)

CROSSREFS

Cf. A000796, A119017, A068425, A117721, A065987, A051480, A007514.

Pi in base b: this sequence (b=2), A004602 (b=3), A004603 (b=4), A004604 (b=5), A004605 (b=6), A004606 (b=7), A006941 (b=8), A004608 (b=9), A000796 (b=10), A068436 (b=11), A068437 (b=12), A068438 (b=13), A068439 (b=14), A068440 (b=15), A062964 (b=16), A060707 (b=60).

Sequence in context: A133100 A216230 A077606 * A114915 A074711 A004585

Adjacent sequences:  A004598 A004599 A004600 * A004602 A004603 A004604

KEYWORD

nonn,base,cons,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified June 27 02:59 EDT 2017. Contains 288777 sequences.