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.

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A154462 Decimal expansion of log_2 (14).

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Oct 30 2009

Keywords

Examples

			3.8073549220576041074419693172318308086410266259661407836772...

Links

Crossrefs

Cf. decimal expansion of log_2(m): A020857 (m=3), A020858 (m=5), A020859 (m=6), A020860 (m=7), A020861 (m=9), A020862 (m=10), A020863 (m=11), A020864 (m=12), A152590 (m=13), this sequence, A154540 (m=15), A154847 (m=17), A154905 (m=18), A154995 (m=19), A155172 (m=20), A155536 (m=21), A155693 (m=22), A155793 (m=23), A155921 (m=24).

Programs

  • Mathematica
    RealDigits[Log[2,14],10,120][[1]] (* Harvey P. Dale, Jul 19 2013 *)

Formula

Equals 1+A020860. - R. J. Mathar, Feb 01 2023

A154540 Decimal expansion of log_2 (15).

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Oct 30 2009

Keywords

Examples

			3.9068905956085185293240583734372066846246458007170616725105...

Links

Crossrefs

Cf. decimal expansion of log_2(m): A020857 (m=3), A020858 (m=5), A020859 (m=6), A020860 (m=7), A020861 (m=9), A020862 (m=10), A020863 (m=11), A020864 (m=12), A152590 (m=13), A154462 (m=14), this sequence, A154847 (m=17), A154905 (m=18), A154995 (m=19), A155172 (m=20), A155536 (m=21), A155693 (m=22), A155793 (m=23), A155921 (m=24).

Programs

  • Mathematica
    RealDigits[Log[2, 15], 10, 100][[1]] (* Vincenzo Librandi, Aug 29 2013 *)

A154905 Decimal expansion of log_2 (18).

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Oct 30 2009

Keywords

Examples

			4.1699250014423123629074778878956330175196288153849621209115...

Links

Crossrefs

Cf. decimal expansion of log_2(m): A020857 (m=3), A020858 (m=5), A020859 (m=6), A020860 (m=7), A020861 (m=9), A020862 (m=10), A020863 (m=11), A020864 (m=12), A152590 (m=13), A154462 (m=14), A154540 (m=15), A154847 (m=17), this sequence, A154995 (m=19), A155172 (m=20), A155536 (m=21), A155693 (m=22), A155793 (m=23), A155921 (m=24).

Programs

  • Mathematica
    RealDigits[Log[2,18],10,120][[1]] (* Harvey P. Dale, Jul 12 2012 *)

Formula

Equals 1 + A020861 = 1 + 2*A020857. - Jianing Song, Nov 16 2024

A154995 Decimal expansion of log_2 (19).

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Oct 30 2009

Keywords

Examples

			4.2479275134435854937935194229068344226935075696615340145815...

Links

Crossrefs

Cf. decimal expansion of log_2(m): A020857 (m=3), A020858 (m=5), A020859 (m=6), A020860 (m=7), A020861 (m=9), A020862 (m=10), A020863 (m=11), A020864 (m=12), A152590 (m=13), A154462 (m=14), A154540 (m=15), A154847 (m=17), A154905 (m=18), this sequence, A155172 (m=20), A155536 (m=21), A155693 (m=22), A155793 (m=23), A155921 (m=24).

Programs

  • Mathematica
    RealDigits[Log[2, 19], 10, 100][[1]] (* Vincenzo Librandi, Aug 29 2013 *)

A155536 Decimal expansion of log_2 (21).

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Oct 30 2009

Keywords

Examples

			4.3923174227787602888957082611796473174008410336586218441330...

Links

Crossrefs

Cf. decimal expansion of log_2(m): A020857 (m=3), A020858 (m=5), A020859 (m=6), A020860 (m=7), A020861 (m=9), A020862 (m=10), A020863 (m=11), A020864 (m=12), A152590 (m=13), A154462 (m=14), A154540 (m=15), A154847 (m=17), A154905 (m=18), A154995 (m=19), A155172 (m=20), this sequence, A155693 (m=22), A155793 (m=23), A155921 (m=24).

Programs

  • Mathematica
    RealDigits[Log[2, 21], 10, 100][[1]] (* Vincenzo Librandi, Aug 29 2013 *)

A155693 Decimal expansion of log_2 (22).

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Oct 30 2009

Keywords

Examples

			4.4594316186372972561993630467257929587032315256817680713128...

Links

Crossrefs

Cf. decimal expansion of log_2(m): A020857 (m=3), A020858 (m=5), A020859 (m=6), A020860 (m=7), A020861 (m=9), A020862 (m=10), A020863 (m=11), A020864 (m=12), A152590 (m=13), A154462 (m=14), A154540 (m=15), A154847 (m=17), A154905 (m=18), A154995 (m=19), A155172 (m=20), A155536 (m=21), this sequence, A155793 (m=23), A155921 (m=24).

Programs

  • Mathematica
    RealDigits[Log[2, 22], 10, 100][[1]] (* Vincenzo Librandi, Aug 29 2013 *)

Formula

Equals 1 + A020863. - Jianing Song, Nov 16 2024

A155793 Decimal expansion of log_2 (23).

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Oct 30 2009

Keywords

Examples

			4.5235619560570128722941482441626688444988251254425550594944...

Links

Crossrefs

Cf. decimal expansion of log_2(m): A020857 (m=3), A020858 (m=5), A020859 (m=6), A020860 (m=7), A020861 (m=9), A020862 (m=10), A020863 (m=11), A020864 (m=12), A152590 (m=13), A154462 (m=14), A154540 (m=15), A154847 (m=17), A154905 (m=18), A154995 (m=19), A155172 (m=20), A155536 (m=21), A155693 (m=22), this sequence, A155921 (m=24).

Programs

  • Mathematica
    RealDigits[Log[2, 23], 10, 100][[1]] (* Vincenzo Librandi, Aug 29 2013 *)

A046104 Denominators of convergents to the diesis log_2(5/4).

Original entry on oeis.org

1, 3, 28, 59, 146, 643, 4004, 8651, 12655, 21306, 76573, 97879, 1838395, 1936274, 13456039, 15392313, 44240665, 59632978, 103873643, 475127550, 579001193, 24793177656, 149338067129, 174131244785, 845863046269, 1865857337323
Offset: 1

Views

Author

Eric W. Weisstein

Keywords

Comments

Also denominators of convergents to log_2(5), cf. A020858. Denominators of convergents to log_2(128/125), sometimes also referred to as diesis, are (1, 29, 117, 263, 643, 906, 1549, 5553, 7102, 90777, ...). - M. F. Hasler, Apr 30 2020

Links

Crossrefs

Cf. A046103 (numerators corresponding to log_2(5/4)), A116985 (numerators corresponding to log_2(5)).

Programs

  • Mathematica
    Denominator[ Table[ ContinuedFraction[ Log[ 5/4 ]/Log[ 2 ], i ]//Normal, {i, 30} ] ]
Denominator[Convergents[Log[2,5/4],30]] (* Harvey P. Dale, Jan 24 2015 *)
  • PARI
    contfracpnqn(contfrac(log(5)/log(2)),99)[2,] \\ M. F. Hasler, Apr 30 2020

Extensions

Name corrected and links edited by M. F. Hasler, Apr 30 2020

A236023 Decimal expansion of log_2 (5) - log_3 (7).

Original entry on oeis.org

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

Views

Author

Jaroslav Krizek, Jan 18 2014

Keywords

Comments

Decimal expansion of minimal value of function gamma(n) = log_2(n+1) - log_tau(n) (sigma(n)) for n = 4, where gamma(n) is called the gamma-deviation from primality of the number n (see A236022).

Examples

			0.550684345725940087802391122406...

Crossrefs

Cf. A236020, A236021, A236022, A236024, A236025, A236026.
Cf. A020858, A152565.

Programs

  • Mathematica
    RealDigits[Log2[5] - Log[3, 7], 10, 120][[1]] (* Amiram Eldar, Jun 06 2023 *)

Formula

Equals log(5)/log(2) - log(7)/log(3) = A020858 - A152565.

A061785 a(n) = m such that 2^m < 5^n < 2^(m+1).

Original entry on oeis.org

2, 4, 6, 9, 11, 13, 16, 18, 20, 23, 25, 27, 30, 32, 34, 37, 39, 41, 44, 46, 48, 51, 53, 55, 58, 60, 62, 65, 67, 69, 71, 74, 76, 78, 81, 83, 85, 88, 90, 92, 95, 97, 99, 102, 104, 106, 109, 111, 113, 116, 118, 120, 123, 125, 127, 130, 132, 134, 136, 139, 141, 143, 146, 148
Offset: 1

Views

Author

Lekraj Beedassy, May 09 2003

Keywords

Comments

The Beatty sequence for log_2(5) (A020858). The asymptotic density of this sequence is log_5(2) (A152675). - Amiram Eldar, Apr 09 2021
One less than the length of 5^n written in binary. Could and should be extended to a(0) = 0 (with definition corrected to "2^m <= ..."). - M. F. Hasler, Apr 17 2024

Examples

			a(2) = 4 since 2^4 < 5^2 < 2^(4+1).

Links

Crossrefs

Cf. A020858, A152675.
Cf. A118738 (Hamming weight of 5^n).

Programs

  • Mathematica
    Table[Floor[n*Log2[5]], {n, 100}] (* Amiram Eldar, Apr 09 2021 *)
  • PARI
    a(n) = floor(n*log(5)/log(2)) \\ Michel Marcus, Jul 27 2013
  • Python
    def A061785(n): return (5**n).bit_length()-1 # Chai Wah Wu, Jul 22 2025

Formula

a(n) = floor(n*log_2(5)). - M. F. Hasler, Apr 17 2024

Extensions

Corrected and extended by John W. Layman, May 09 2003
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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