cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 21-25 of 25 results.

A155979 Decimal expansion of log_10 (24).

Original entry on oeis.org

1, 3, 8, 0, 2, 1, 1, 2, 4, 1, 7, 1, 1, 6, 0, 6, 0, 2, 2, 9, 3, 6, 2, 4, 4, 5, 8, 7, 4, 2, 8, 5, 9, 4, 3, 8, 9, 5, 0, 4, 6, 9, 8, 5, 0, 8, 5, 7, 7, 0, 2, 1, 4, 8, 8, 7, 6, 1, 1, 4, 8, 0, 2, 3, 6, 8, 6, 5, 5, 3, 7, 2, 0, 6, 0, 6, 9, 3, 4, 6, 5, 1, 5, 0, 3, 7, 5, 0, 1, 1, 2, 0, 0, 2, 1, 7, 4, 8, 1
Offset: 1

Views

Author

N. J. A. Sloane, Oct 30 2009

Keywords

Examples

			1.3802112417116060229362445874285943895046985085770214887611...

Links

Crossrefs

Cf. decimal expansion of log_10(m): A007524 (m=2), A114490 (m=3), A114493 (m=4), A153268 (m=5), A153496 (m=6), A153620 (m=7), A153790 (m=8), A104139 (m=9), A154182 (m=11), A154203 (m=12), A154368 (m=13), A154478 (m=14), A154580 (m=15), A154794 (m=16), A154860 (m=17), A154953 (m=18), A155062 (m=19), A155522 (m=20), A155677 (m=21), A155746 (m=22), A155830 (m=23).

Programs

A210434 Number of digits in 4^n.

Original entry on oeis.org

1, 1, 2, 2, 3, 4, 4, 5, 5, 6, 7, 7, 8, 8, 9, 10, 10, 11, 11, 12, 13, 13, 14, 14, 15, 16, 16, 17, 17, 18, 19, 19, 20, 20, 21, 22, 22, 23, 23, 24, 25, 25, 26, 26, 27, 28, 28, 29, 29, 30, 31, 31, 32, 32, 33, 34, 34, 35, 35, 36, 37, 37, 38, 38, 39, 40, 40, 41, 41
Offset: 0

Views

Author

Luc Comeau-Montasse, Mar 21 2012

Keywords

Comments

Since log10(4) = A114493 ~ 0.60205 (= twice log10(2) = 0.30102999566...), the first 98 terms are equal to floor(n*3/5)+1. - M. F. Hasler, Mar 31 2025

Examples

			a(4) = 3 because 4^4 = 256, which has 3 digits.
a(5) = 4 because 4^5 = 1024, which has 4 digits.

Links

Crossrefs

Cf. A000302, A034887, A034888, A210062, A210435, A210436.

Programs

  • Magma
    [#Intseq(4^n): n in [0..68]]; // Bruno Berselli, Mar 22 2012
  • Maple
    a:= n-> length(4^n): seq(a(n), n=0..100); # Alois P. Heinz, Mar 22 2012
  • Mathematica
    Table[Length[IntegerDigits[4^n]], {n, 0, 68}] (* Bruno Berselli, Mar 22 2012 *)
  • PARI
    apply( {A210434(n)=logint(4^n,10)+1}, [0..66]) \\ M. F. Hasler, Mar 31 2025
  • PARI
    a(n)=log(4)*n\log(10)+1 \\ correct up to n ~ 10^precision, with default precision = 38. - M. F. Hasler, Mar 31 2025
  • Python
    from math import log
def A210434(n): return int(n*log(4,10))+1 if n<1e16 else "not enough precision" # M. F. Hasler, Mar 31 2025

Formula

a(n) = A055642(A000302(n)) = A055642(4^n) = floor(log_10(10*(4^n))). - Jonathan Vos Post, Mar 22 2012

A385659 Decimal expansion of log_10(1 + 1/3).

Original entry on oeis.org

1, 2, 4, 9, 3, 8, 7, 3, 6, 6, 0, 8, 2, 9, 9, 9, 5, 3, 1, 3, 2, 4, 4, 9, 8, 8, 6, 1, 9, 3, 8, 7, 0, 7, 4, 4, 3, 3, 6, 2, 5, 0, 8, 9, 8, 7, 3, 3, 5, 2, 1, 2, 1, 7, 7, 9, 0, 9, 8, 9, 2, 8, 1, 9, 4, 8, 9, 8, 7, 2, 2, 5, 7, 6, 5, 1, 8, 7, 8, 9, 5, 9, 3, 0, 8, 8, 6
Offset: 0

Views

Author

Marco Ripà, Jul 06 2025

Keywords

Comments

Probability that 3 occurs as the first significant digit in data collections according to Benford's law (see A007524).

Examples

			0.12493873660829995313244988619...

Links

Crossrefs

Benford's law for digit: A007524 (1), A104140 (9), A154203 (5), A154580 (2).

Programs

  • Mathematica
    RealDigits[Log[10, 4/3], 10, 90][[1]]

Formula

Equals A114493 - A114490. - R. J. Mathar, Jul 13 2025

Extensions

a(16) to a(86) corrected by Marco Ripà, Jul 12 2025

A114466 Number of decimal digits in the 10^n-th Catalan number.

Original entry on oeis.org

1, 5, 57, 598, 6015, 60199, 602051, 6020590, 60205987, 602059978, 6020599899, 60205999117, 602059991310, 6020599913260, 60205999132775, 602059991327940, 6020599913279600, 60205999132796214
Offset: 0

Views

Author

Eric W. Weisstein, Nov 29 2005

Keywords

Links

Crossrefs

Cf. A000108, A114493.

Programs

  • Mathematica
    Table[IntegerLength[CatalanNumber[10^n]], {n, 0, 9}] (* The program generates the first 10 terms of the sequence. To generate more, increase the "9" constant but the program may take a long time to run. *) (* Harvey P. Dale, Sep 01 2021 *)

Extensions

Edited by Charles R Greathouse IV, Aug 05 2010

A114501 Number of decimal digits in binomial(2*10^n, 10^n).

Original entry on oeis.org

1, 6, 59, 601, 6019, 60204, 602057, 6020597, 60205995, 602059987, 6020599909, 60205999128, 602059991322, 6020599913273, 60205999132789, 602059991327955, 6020599913279616, 60205999132796231
Offset: 0

Views

Author

Eric W. Weisstein, Dec 01 2005

Keywords

Links

Crossrefs

Cf. A000984, A114493.
Previous Showing 21-25 of 25 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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