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 1-5 of 5 results.

A203125 Decimal expansion of (1/8)! = Gamma(9/8).

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Dec 29 2011

Keywords

Examples

			.94174269984970148808740373015189170307630244851863449262289...

Links

Crossrefs

Cf. A068467, A202623, A203126, A203142.

Programs

Formula

Equals A203142/8. - R. J. Mathar, Jan 15 2021
A203144 *this *A231863 *A011006 = A068467. - R. J. Mathar, Jan 15 2021
Equals Integral_{x=0..oo} exp(-x^8) dx. - Ilya Gutkovskiy, Sep 18 2021

A329219 Decimal expansion of 2^(10/12) = 2^(5/6).

Original entry on oeis.org

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

Views

Author

Jianing Song, Nov 08 2019

Keywords

Comments

2^(10/12) is the ratio of the frequencies of the pitches in a minor seventh (e.g., D4-C5) in 12-tone equal temperament.

Examples

			1.78179743...

Links

Crossrefs

Frequency ratios of musical intervals:
Perfect unison: 2^(0/12) = 1.0000000000
Minor second: 2^(1/12) = 1.0594630943... (A010774)
Major second: 2^(2/12) = 1.1224620483... (A010768)
Minor third: 2^(3/12) = 1.1892071150... (A010767)
Major third: 2^(4/12) = 1.2599210498... (A002580)
Perfect fourth: 2^(5/12) = 1.3348398541... (A329216)
Aug. fourth/
Dim. fifth: 2^(6/12) = 1.4142135623... (A002193)
Perfect fifth: 2^(7/12) = 1.4983070768... (A328229)
Minor sixth: 2^(8/12) = 1.5874010519... (A005480)
Major sixth: 2^(9/12) = 1.6817928305... (A011006)
Minor seventh: 2^(10/12) = 1.7817974362... (this sequence)
Major seventh: 2^(11/12) = 1.8877486253... (A329220)
Perfect octave: 2^(12/12) = 2.0000000000

Programs

  • Mathematica
    First[RealDigits[2^(5/6), 10, 100]] (* Paolo Xausa, Apr 27 2024 *)
  • PARI
    default(realprecision, 100); 2^(10/12)

Formula

Equals 2/A010768.
Equals Product_{k>=0} (1 + (-1)^k/(6*k + 1)). - Amiram Eldar, Jul 25 2020

A329216 Decimal expansion of 2^(5/12).

Original entry on oeis.org

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

Views

Author

Jianing Song, Nov 08 2019

Keywords

Comments

2^(5/12) is the ratio of the frequencies of the pitches in a perfect fourth (e.g., D4-G4) in 12-tone equal temperament.

Links

Crossrefs

Frequency ratios of musical intervals:
Perfect unison: 2^(0/12) = 1.0000000000
Minor second: 2^(1/12) = 1.0594630943... (A010774)
Major second: 2^(2/12) = 1.1224620483... (A010768)
Minor third: 2^(3/12) = 1.1892071150... (A010767)
Major third: 2^(4/12) = 1.2599210498... (A002580)
Perfect fourth: 2^(5/12) = 1.3348398541... (this sequence)
Aug. fourth/
Dim. fifth: 2^(6/12) = 1.4142135623... (A002193)
Perfect fifth: 2^(7/12) = 1.4983070768... (A328229)
Minor sixth: 2^(8/12) = 1.5874010519... (A005480)
Major sixth: 2^(9/12) = 1.6817928305... (A011006)
Minor seventh: 2^(10/12) = 1.7817974362... (A329219)
Major seventh: 2^(11/12) = 1.8877486253... (A329220)
Perfect octave: 2^(12/12) = 2.0000000000

Programs

  • Mathematica
    First[RealDigits[2^(5/12), 10, 100]] (* Paolo Xausa, Apr 28 2024 *)
  • PARI
    default(realprecision, 100); 2^(5/12)

Formula

Equals 2/A328229.

A329220 Decimal expansion of 2^(11/12).

Original entry on oeis.org

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

Views

Author

Jianing Song, Nov 08 2019

Keywords

Comments

2^(11/12) is the ratio of the frequencies of the pitches in a major seventh (e.g., D4-C#5) in 12-tone equal temperament.

Links

Crossrefs

Frequency ratios of musical intervals:
Perfect unison: 2^(0/12) = 1.0000000000
Minor second: 2^(1/12) = 1.0594630943... (A010774)
Major second: 2^(2/12) = 1.1224620483... (A010768)
Minor third: 2^(3/12) = 1.1892071150... (A010767)
Major third: 2^(4/12) = 1.2599210498... (A002580)
Perfect fourth: 2^(5/12) = 1.3348398541... (A329216)
Aug. fourth/
Dim. fifth: 2^(6/12) = 1.4142135623... (A002193)
Perfect fifth: 2^(7/12) = 1.4983070768... (A328229)
Minor sixth: 2^(8/12) = 1.5874010519... (A005480)
Major sixth: 2^(9/12) = 1.6817928305... (A011006)
Minor seventh: 2^(10/12) = 1.7817974362... (A329219)
Major seventh: 2^(11/12) = 1.8877486253... (this sequence)
Perfect octave: 2^(12/12) = 2.0000000000

Programs

  • Mathematica
    First[RealDigits[2^(11/12), 10, 100]] (* Paolo Xausa, Apr 28 2024 *)
  • PARI
    default(realprecision, 100); 2^(11/12)

Formula

Equals 2/A010774.
Equals Product_{k>=0} (1 + (-1)^k/(12*k + 1)). - Amiram Eldar, Jul 29 2020

A386590 Decimal expansion of the absolute value of zeta(1/4).

Original entry on oeis.org

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

Views

Author

Artur Jasinski, Jul 26 2025

Keywords

Examples

			0.81327840526189165652144782007352557448157...

Crossrefs

Cf. A251734, A385423.

Programs

  • Maple
    evalf(abs(Zeta(1/4)), 120);  # Alois P. Heinz, Jul 26 2025
  • Mathematica
    RealDigits[-Zeta[1/4], 10, 105][[1]]
  • PARI
    -zeta(1/4) \\ Stefano Spezia, Aug 03 2025

Formula

Sum_{k>=1} (-1)^(k+1)/k^(1/4) = |Zeta(1/4)| * (2^(3/4)-1) = this * (A011006 -1).
Showing 1-5 of 5 results.

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

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