A004601 -id:A004601 - cp's OEIS frontend

A004603 Expansion of Pi in base 4.

3, 0, 2, 1, 0, 0, 3, 3, 3, 1, 2, 2, 2, 2, 0, 2, 0, 2, 0, 1, 1, 2, 2, 0, 3, 0, 0, 2, 0, 3, 1, 0, 3, 0, 1, 0, 3, 0, 1, 2, 1, 2, 0, 2, 2, 0, 2, 3, 2, 0, 0, 0, 3, 1, 3, 0, 0, 1, 3, 0, 3, 1, 0, 1, 0, 2, 2, 1, 0, 0, 0, 2, 1, 0, 3, 2, 0, 0, 2, 0, 2, 0, 2, 2, 1, 2, 1, 3, 3, 0, 3, 0, 1, 3, 1, 0, 0, 0, 0, 2, 0, 0, 2, 3, 2

Offset: 1

N. J. A. Sloane

Theoretically, this sequence could be used to encode a given number of digits of Pi as a DNA sequence, which could then be read back from one helix. The value read back from the other helix would of course depend on the assignment of G, A, C, T to the digits 0, 1, 2, 3. - Alonso del Arte, Nov 07 2011

			3.02100333122220202011220300203103010301...

G. C. Greubel, Table of n, a(n) for n = 1..10000
Francisco Javier Aragón Artacho, 100 billion step walk on the digits of pi
F. J. Aragon Artacho, D. H. Bailey, J. M. Borwein, P. B. Borwein, J. Fountain, and M. Skerritt Walking on numbers: a multiple media mathematics project, 2012.
Elias Bröms, Pictures of Pi

Pi in base b: A004601 (b=2), A004602 (b=3), this sequence (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).
Cf. A007514.
Cf. A004595, A004541. - Jason Kimberley, Dec 01 2012

RealDigits[Pi, 4, 100][[1]]
Table[ResourceFunction["NthDigit"][Pi, n, 4], {n, 1, 100}] (* Joan Ludevid, Jul 04 2022; easy to compute a(10000000)=2 with this function; requires Mathematica 12.0+ *)

a(n) = 2*A004601(2n) + A004601(2n+1). - Jason Kimberley, Nov 08 2012

A060707 Base-60 (Babylonian or sexagesimal) expansion of Pi.

Original entry on oeis.org

3, 8, 29, 44, 0, 47, 25, 53, 7, 24, 57, 36, 17, 43, 4, 29, 7, 10, 3, 41, 17, 52, 36, 12, 14, 36, 44, 51, 50, 15, 33, 7, 23, 59, 9, 13, 48, 22, 12, 21, 45, 22, 56, 47, 39, 44, 28, 37, 58, 23, 21, 11, 56, 33, 22, 40, 42, 31, 6, 6, 3, 46, 16, 52, 2, 48, 33, 24, 38, 33, 22, 1, 0, 1

Offset: 1

Robert G. Wilson v, Feb 05 2001

Mohammad K. Azarian, Al-Risala al-Muhitiyya: A Summary, Missouri Journal of Mathematical Sciences, Vol. 22, No. 2, 2010, pp. 64-85.
Mohammad K. Azarian, The Introduction of Al-Risala al-Muhitiyya: An English Translation, International Journal of Pure and Applied Mathematics, Vol. 57, No. 6, 2009, pp. 903-914.
Mohammad K. Azarian, Al-Kashi's Fundamental Theorem, International Journal of Pure and Applied Mathematics, Vol. 14, No. 4, 2004, pp. 499-509. Mathematical Reviews, MR2005b:01021 (01A30), February 2005, p. 919. Zentralblatt MATH, Zbl 1059.01005.
Mohammad K. Azarian, Meftah al-hesab: A Summary, MJMS, Vol. 12, No. 2, Spring 2000, pp. 75-95. Mathematical Reviews, MR 1 764 526. Zentralblatt MATH, Zbl 1036.01002.
Mohammad K. Azarian, A Summary of Mathematical Works of Ghiyath ud-din Jamshid Kashani, Journal of Recreational Mathematics, Vol. 29(1), pp. 32-42, 1998.

Harry J. Smith, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Pi Digits

Cf. A000796, A091649, A159991.

Pi in base b: A004601 (b=2), A004602 (b=3), A004603 (b=4), this sequence (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). - Jason Kimberley, Dec 06 2012

Mathematica
```
RealDigits[ Pi, 60, 75][[1]]
```

{ default(realprecision, 17900); x=Pi; for (n=1, 10000, d=floor(x); x=(x-d)*60; write("b060707.txt", n, " ", d)); } \\ Harry J. Smith, Jul 09 2009

A068440 Expansion of Pi in base 15.

Original entry on oeis.org

3, 2, 1, 12, 13, 1, 13, 12, 4, 6, 12, 2, 11, 7, 14, 5, 0, 8, 4, 8, 4, 7, 7, 3, 14, 0, 6, 9, 1, 9, 13, 1, 14, 5, 0, 9, 6, 3, 13, 11, 7, 9, 12, 6, 9, 7, 3, 9, 14, 10, 3, 7, 3, 1, 14, 7, 9, 12, 13, 14, 1, 0, 10, 8, 14, 13, 4, 12, 6, 3, 0, 10, 8, 3, 11, 9, 11, 5, 13, 10, 4, 6, 4, 10, 9, 1, 5, 2

Offset: 1

Benoit Cloitre, Mar 09 2002

			3.21cd1dc46c2b...

G. C. Greubel, Table of n, a(n) for n = 1..10000

Pi in base b: A004601 (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), this sequence (b=15), A062964 (b=16), A060707 (b=60).

Cf. A007514.

RealDigits[ N[ Pi, 115], 15] [[1]]
RealDigits[Pi,15,120][[1]] (* Harvey P. Dale, Aug 05 2025 *)

A004593 Expansion of e in base 2.

Original entry on oeis.org

1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1

Offset: 2

N. J. A. Sloane

The first 19 digits are a reverse copy of the 7th through 25th digits of the binary expansion of Pi (A004601). - Dan Graham, May 03 2015

			10.10110111111000010...

Vincenzo Librandi, Table of n, a(n) for n = 2..2000

Expansion of e in base b: this sequence (b=2), A004594 (b=3), A004595 (b=4), A004596 (b=5), A004597 (b=6), A004598 (b=7), A004599 (b=8), A004600 (b=9), A001113 (b=10), A170873 (b=16). - Jason Kimberley, Dec 05 2012

First@ RealDigits[N[E, 120], 2] (* Michael De Vlieger, May 05 2015 *)

a(n)=exp(1)*2^(n-3)\1%2 \\ Charles R Greathouse IV, May 05 2015

A068436 Expansion of Pi in base 11.

Original entry on oeis.org

3, 1, 6, 1, 5, 0, 7, 0, 2, 8, 6, 5, 10, 4, 8, 5, 2, 3, 5, 2, 1, 5, 2, 5, 9, 7, 7, 7, 5, 2, 9, 4, 1, 8, 3, 8, 6, 6, 8, 8, 4, 8, 8, 5, 3, 1, 6, 3, 10, 1, 10, 5, 4, 2, 1, 3, 0, 0, 4, 6, 5, 8, 0, 6, 5, 2, 2, 7, 3, 5, 0, 5, 3, 3, 7, 1, 5, 2, 7, 1, 7, 8, 1, 10, 6, 5, 6, 3, 7, 1, 5, 7, 8, 1, 3, 3, 4, 9, 2, 8, 8, 8

Offset: 1

Benoit Cloitre, Mar 09 2002

			3.16150702865a4...

Pi in base b: A004601 (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), this sequence (b=11), A068437 (b=12), A068438 (b=13), A068439 (b=14), A068440 (b=15), A062964 (b=16), A060707 (b=60).

Cf. A007514.

RealDigits[Pi, 11, 111][[1]]
Table[ResourceFunction["NthDigit"][Pi, n, 11], {n, 1, 111}] (* Joan Ludevid, Oct 09 2022 easy to compute a(10000000)=10 with this function; requires Mathematica 12.0+ *)

A068437 Expansion of Pi in base 12.

Original entry on oeis.org

3, 1, 8, 4, 8, 0, 9, 4, 9, 3, 11, 9, 1, 8, 6, 6, 4, 5, 7, 3, 10, 6, 2, 1, 1, 11, 11, 1, 5, 1, 5, 5, 1, 10, 0, 5, 7, 2, 9, 2, 9, 0, 10, 7, 8, 0, 9, 10, 4, 9, 2, 7, 4, 2, 1, 4, 0, 10, 6, 0, 10, 5, 5, 2, 5, 6, 10, 0, 6, 6, 1, 10, 0, 3, 7, 5, 3, 10, 3, 10, 10, 5, 4, 8, 0, 5, 6, 4, 6, 8, 8, 0, 1, 8, 1, 10, 3

Offset: 1

Benoit Cloitre, Mar 09 2002

			3.184809493b918664573b6211bb151551a05729...

Michael De Vlieger, Table of n, a(n) for n = 1..10368 (decimal 10,368 = duodecimal 6000 or 6 * 12^3)
V. Ponomarenko, The Music of Pi, Amer. Math. Monthly, 119 (No. 8, 2012), p. 711. - _N. J. A. Sloane_, Oct 13 2012

Pi in base b: A004601 (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), this sequence (b=12), A068438 (b=13), A068439 (b=14), A068440 (b=15), A062964 (b=16), A060707 (b=60).

Cf. A007514.

RealDigits[Pi,12,120][[1]] (* Harvey P. Dale, Jul 04 2014 *)
Table[ResourceFunction["NthDigit"][Pi, n, 12], {n, 1, 120}] (* Joan Ludevid, Oct 11 2022; easy to compute a(10000000)=8 with this function; requires Mathematica 12.0+ *)

A004605 Expansion of Pi in base 6.

Original entry on oeis.org

3, 0, 5, 0, 3, 3, 0, 0, 5, 1, 4, 1, 5, 1, 2, 4, 1, 0, 5, 2, 3, 4, 4, 1, 4, 0, 5, 3, 1, 2, 5, 3, 2, 1, 1, 0, 2, 3, 0, 1, 2, 1, 4, 4, 4, 2, 0, 0, 4, 1, 1, 5, 2, 5, 2, 5, 5, 3, 3, 1, 4, 2, 0, 3, 3, 3, 1, 3, 1, 1, 3, 5, 5, 3, 5, 1, 3, 1, 2, 3, 3, 4, 5, 5, 3, 3, 4, 1, 0, 0, 1, 5, 1, 5, 4, 3, 4, 4, 4, 0, 1, 2, 3, 4, 3

Offset: 1

N. J. A. Sloane

			3.05033005141512410523441405312532110230...

G. C. Greubel, Table of n, a(n) for n = 1..10000

Pi in base b: A004601 (b=2), A004602 (b=3), A004603 (b=4), A004604 (b=5), this sequence (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).

Cf. A007514.

RealDigits[Pi, 6, 105][[1]]
Table[ResourceFunction["NthDigit"][Pi, n, 6], {n, 1, 105}] (* Joan Ludevid ,Aug 17 2022;easy to compute a(10000000)=0 with this function;requires Mathematica 12.0+ *)

A004604 Expansion of Pi in base 5.

Original entry on oeis.org

3, 0, 3, 2, 3, 2, 2, 1, 4, 3, 0, 3, 3, 4, 3, 2, 4, 1, 1, 2, 4, 1, 2, 2, 4, 0, 4, 1, 4, 0, 2, 3, 1, 4, 2, 1, 1, 1, 4, 3, 0, 2, 0, 3, 1, 0, 0, 2, 2, 0, 0, 3, 4, 4, 4, 1, 3, 2, 2, 1, 1, 0, 1, 0, 4, 0, 3, 3, 2, 1, 3, 4, 4, 0, 0, 4, 3, 2, 4, 4, 4, 0, 1, 4, 4, 1, 0, 4, 2, 3, 3, 4, 1, 3, 3, 0, 1, 1, 3, 2

Offset: 1

N. J. A. Sloane

			3.03232214303343241124122404140231421114...

G. C. Greubel, Table of n, a(n) for n = 1..10000
Wadim Zudilin, A BBP-style computation for π in base 5, arXiv:2409.10097 [math.NT], 2024.

Pi in base b: A004601 (b=2), A004602 (b=3), A004603 (b=4), this sequence (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).

Cf. A007514.

RealDigits[Pi, 5, 100][[1]]
Table[ResourceFunction["NthDigit"][Pi, n, 5], {n, 1, 100}] (* Joan Ludevid, Aug 17 2022;easy to compute a(10000000)=0 with this function;requires Mathematica 12.0+ *)

A004606 Expansion of Pi in base 7.

Original entry on oeis.org

3, 0, 6, 6, 3, 6, 5, 1, 4, 3, 2, 0, 3, 6, 1, 3, 4, 1, 1, 0, 2, 6, 3, 4, 0, 2, 2, 4, 4, 6, 5, 2, 2, 2, 6, 6, 4, 3, 5, 2, 0, 6, 5, 0, 2, 4, 0, 1, 5, 5, 4, 4, 3, 2, 1, 5, 4, 2, 6, 4, 3, 1, 0, 2, 5, 1, 6, 1, 1, 5, 4, 5, 6, 5, 2, 2, 0, 0, 0, 2, 6, 2, 2, 4, 3, 6, 1, 0, 3, 3, 0, 1, 4, 4, 3, 2, 3, 3, 6, 3, 1, 0, 1, 1, 3

Offset: 1

N. J. A. Sloane

			3.06636514320361341102634022446522266435...

G. C. Greubel, Table of n, a(n) for n = 1..10000

Pi in base b: A004601 (b=2), A004602 (b=3), A004603 (b=4), A004604 (b=5), A004605 (b=6), this sequence (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).

Cf. A007514.

RealDigits[Pi, 7, 105][[1]]
Table[ResourceFunction["NthDigit"][Pi, n, 7], {n, 1, 105}] (* Joan Ludevid, Sep 13 2022; easy to compute a(10000000)=5 with this function;requires Mathematica 12.0+ *)

A006941 Expansion of Pi in base 8.

Original entry on oeis.org

3, 1, 1, 0, 3, 7, 5, 5, 2, 4, 2, 1, 0, 2, 6, 4, 3, 0, 2, 1, 5, 1, 4, 2, 3, 0, 6, 3, 0, 5, 0, 5, 6, 0, 0, 6, 7, 0, 1, 6, 3, 2, 1, 1, 2, 2, 0, 1, 1, 1, 6, 0, 2, 1, 0, 5, 1, 4, 7, 6, 3, 0, 7, 2, 0, 0, 2, 0, 2, 7, 3, 7, 2, 4, 6, 1, 6, 6, 1, 1, 6, 3, 3, 1, 0, 4, 5, 0, 5, 1, 2, 0, 2, 0, 7, 4, 6, 1, 6, 1, 5, 0, 0, 2, 3

Offset: 1

N. J. A. Sloane

			3.1103755242102643021514230630505600670...

D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, Vol. 1, p. 614.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

G. C. Greubel, Table of n, a(n) for n = 1..10000
Index entries for sequences related to the number Pi

Pi in base b: A004601 (b=2), A004602 (b=3), A004603 (b=4), A004604 (b=5), A004605 (b=6), A004606 (b=7), this sequence (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).

Cf. A007514.

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

RealDigits[ N[ Pi, 105], 8] [[1]]
Table[ResourceFunction["NthDigit"][Pi, n, 8], {n, 1, 105}] (* Joan Ludevid, Sep 13 2022; easy to compute a(10000000)=1 with this function; requires Mathematica 12.0+ *)

a(n) = 4*A004601(3n) + 2*A004601(3n+1) + 1*A004601(3n+2). - Jason Kimberley, Nov 06 2012

More terms from Michel ten Voorde, Apr 14 2001

cp's OEIS Frontend

A004603 Expansion of Pi in base 4.

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A060707 Base-60 (Babylonian or sexagesimal) expansion of Pi.

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A068440 Expansion of Pi in base 15.

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A004593 Expansion of e in base 2.

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PARI

A068436 Expansion of Pi in base 11.

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A068437 Expansion of Pi in base 12.

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A004605 Expansion of Pi in base 6.

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A004604 Expansion of Pi in base 5.

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A004606 Expansion of Pi in base 7.

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