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

Author

N. J. A. Sloane

Keywords

• nonn
• base
• cons
• easy

Examples

			11.0010010000111111011010101000100010000...
		

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]

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).

Programs

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+ *)

PARI

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