A119017 -id:A119017 - cp's OEIS frontend

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

N. J. A. Sloane

			11.0010010000111111011010101000100010000...

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

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]

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).

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

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
```

A119377 Numbers k such that the next k binary digits of Pi are odd primes with no leading zeros.

Original entry on oeis.org

2787, 6, 7, 23, 2, 3, 3, 8, 2, 2, 2, 5, 8, 2, 18, 9, 10, 413, 8, 3, 2, 4019, 14, 4, 2, 2, 11, 21, 4, 2, 3, 6, 2, 11, 3, 5, 19, 2, 6, 2, 4, 32, 2, 56, 31, 6, 7, 7, 2, 32, 20, 9, 10, 900, 2, 2, 2, 97, 5, 2, 8, 64, 3, 13, 3, 2, 6, 7, 15, 3, 2666, 7, 8, 3, 14, 3, 2, 2, 6, 5, 92, 17, 31, 4, 241, 78, 3

Offset: 1

Robert G. Wilson v, Jul 24 2006

Partition the string of binary digits of Pi in such a way that each partition begins and ends with 1 (thus no leading or trailing zeros) and each such partition is prime.
Pi_2 = 1100100100001111110110101010001000100001011010001100001000..._2 (A004601).
If 2 is allowed as a member, then the sequence begins: 2787,2,5,6,2,2,2,39,5,8,2,18,9,10,2,153,2,6,2,18,7,7,12,2,2,2,2,....

			a(1) represents the binary number 1100100100...(2767 terms)...0100000011 which equals the decimal number 7339860347...(819 terms)...8308318467 which is a prime.
a(2) represents the binary number 101001 which equals the decimal number 41, a prime.

Cf. A004601, A068425, A117721, A065987, A119017.

ps = First@ RealDigits[Pi, 2, 12010]; lst = {}; Do[k = 1; While[fd = FromDigits[ Take[ps, k], 2]; EvenQ@fd || ps[[k + 1]] == 0 || !PrimeQ@fd, k++ ]; AppendTo[lst, k]; ps = Drop[ps, k], {n, 87}]; lst

cp's OEIS Frontend

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

Views

Author

Keywords

Examples

References

Links

Crossrefs

Programs

Maple

Mathematica

PARI