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.

Showing 1-4 of 4 results.

A154434 Decimal expansion of log_21 (13).

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Oct 30 2009

Keywords

Examples

			.84248003091726510655878049884008339833348686470762097554384...

Links

Crossrefs

Cf. decimal expansion of log_21(m): A152825 (m=2), A153097 (m=3), A153131 (m=4), A153455 (m=5), A153611 (m=6), A153632 (m=7), A153895 (m=8), A154020 (m=9), A154171 (m=10), A154192 (m=11), A154213 (m=12), this sequence, A154499 (m=14), A154707 (m=15), A154839 (m=16), A154901 (m=17), A154977 (m=18), A155129 (m=19), A155532 (m=20), A155790 (m=22), A155909 (m=23), A156028 (m=24).

Programs

  • Mathematica
    RealDigits[Log[21, 13], 10, 100][[1]] (* Vincenzo Librandi, Sep 07 2013 *)

Formula

Equals A016636 / A016644. - R. J. Mathar, Jul 13 2025

A016449 Continued fraction for log(21).

Original entry on oeis.org

3, 22, 2, 5, 1, 5, 2, 1, 3, 2, 5, 2, 1, 9, 4, 1, 2, 26, 1, 1, 1, 51, 1, 2, 7, 11, 1, 1, 1, 10, 4, 1, 6, 19, 5, 1, 1, 3, 2, 6, 1, 5, 2, 3, 20, 11, 7, 2, 2, 1, 5, 1, 4, 1, 1, 1, 1, 1, 1, 18, 1, 13, 3, 2, 2, 3, 4, 3, 4, 1, 2, 10, 1, 6, 28, 7
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Examples

			3.04452243772342299650059798... = 3 + 1/(22 + 1/(2 + 1/(5 + 1/(1 + ...)))). - _Harry J. Smith_, May 17 2009

Links

Crossrefs

Cf. A016644 Decimal expansion. - Harry J. Smith, May 17 2009

Programs

  • Mathematica
    ContinuedFraction[Log[21], 100] (* Paolo Xausa, Mar 22 2024 *)
  • PARI
    { allocatemem(932245000); default(realprecision, 21000); x=contfrac(log(21)); for (n=1, 20000, write("b016449.txt", n, " ", x[n])); } \\ Harry J. Smith, May 17 2009

A016587 Decimal expansion of log(21/2).

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane

Keywords

Examples

			2.351375257163477687083365858907528866209075153044355386073404474081680...

Links

Crossrefs

Cf. A016538 (continued fraction).
Cf. A002162 (log(2)), A016644 (log(21)).

Programs

  • Magma
    SetDefaultRealField(RealField(100)); Log(21/2); // Vincenzo Librandi, Apr 07 2020
  • Mathematica
    RealDigits[Log[21/2], 10, 120][[1]] (* Vincenzo Librandi, Apr 07 2020 *)
  • PARI
    default(realprecision, 20080); x=log(21/2); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b016587.txt", n, " ", d)); \\ Harry J. Smith, May 26 2009

Formula

Equals A016644 - A002162. - Michel Marcus, Apr 07 2020

A386732 Decimal expansion of Integral_{x>=2} 1/(x^12-1) dx.

Original entry on oeis.org

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

Views

Author

Jason Bard, Jul 31 2025

Keywords

Examples

			0.000044394388389732931619793708861045902941185047688518...

Links

Crossrefs

Cf. A016644, A105199, A123868, A304656.

Programs

  • Mathematica
    Join[{0, 0, 0, 0}, RealDigits[1/72 (-4 (3 + Sqrt[3]) Pi + 3 (4 ArcTan[2] + 2 Sqrt[3] ArcTan[5/Sqrt[3]] + 2 ArcTan[4 - Sqrt[3]] + 2 ArcTan[4 + Sqrt[3]] + Log[21] - Sqrt[3] Log[5 - 2 Sqrt[3]] + Sqrt[3] Log[5 + 2 Sqrt[3]])), 10, 100][[1]]]
(* or *)
Join[{0, 0, 0, 0}, RealDigits[Integrate[1/(x^12 - 1), {x, 2, Infinity}], 10, 100][[1]]]
(* or *)
Join[{0, 0, 0, 0}, RealDigits[1/22528*Hypergeometric2F1[11/12, 1, 23/12, 1/4096], 10, 100][[1]]]

Formula

Equals (1/22528) * hypergeometric(11/12, 1; 23/12; 1/4096).
Equals (-6*Pi - 4*sqrt(3)*Pi + 12*arctan(2) - 3*arctan(12/5) + 6*sqrt(3) * arctan(5/sqrt(3)) + 6*sqrt(3) * arctanh((2*sqrt(3))/5) + log(9261))/72.
Showing 1-4 of 4 results.

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

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