A004601 Expansion of Pi in base 2 (or, binary expansion of Pi).

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

Offset

2,1

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 décimales de pi en base 2 jusqu'à 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) [link was dead, retrieved from the Internet archive]

Example

11.0010010000111111011010101000100010000...

Maple

convert(evalf(Pi), binary, 120);  # Alois P. Heinz, Dec 16 2018

Mathematica

RealDigits[Pi, 2, 75][[1]]
Table[ResourceFunction["NthDigit"][Pi, n, 2], {n, 1, 100}] (* Joan Ludevid, Jun 24 2022; easy to compute a(10000000)=0 with this function; requires Mathematica 12.0+ *)

Prog

(PARI) binary(Pi) \\ Altug Alkan, Apr 08 2018

Crossrefs

Cf. 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 * A074937 A267418 A263919

Adjacent sequences: A004598 A004599 A004600 * A004602 A004603 A004604

Keyword

nonn,base,cons,easy

Author

N. J. A. Sloane

Status

approved