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 1-6 of 6 results.

A074921 Decimal expansion of (Pi + e)/2 - sqrt(Pi*e).

Original entry on oeis.org

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

Views

Author

Zak Seidov, Oct 02 2002

Keywords

Examples

			(Pi + e)/2 - sqrt(Pi*e) = 2.9299372410244192369... - 2.92228236532227786454... = 0.0076548757021413723...

Crossrefs

Cf. A019645, A074916.

Programs

  • Mathematica
    Join[{0, 0}, RealDigits[(Pi + E)/2 - Sqrt[Pi*E], 10, 120][[1]]] (* Amiram Eldar, May 07 2023 *)
  • Maxima
    fpprec : 100$ ev(bfloat((%pi+%e)/2-(%pi*%e)^(1/2))); /*Martin Ettl, Oct 16 2012 */

A074948 Decimal representation of sqrt((Pi^2 + e^2)/2).

Original entry on oeis.org

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

Views

Author

Zak Seidov, Oct 05 2002

Keywords

Examples

			sqrt[(Pi^2 + e^2)/2] = 2.93757216932793...

Links

Crossrefs

Cf. A074916, A074917, A074921.

Programs

  • Mathematica
    RealDigits[Sqrt[(Pi^2 + E^2)/2], 10, 50][[1]] (* G. C. Greubel, Jan 10 2017 *)
  • PARI
    sqrt((Pi^2 + exp(2))/2) \\ Michel Marcus, Oct 03 2013

A074950 Decimal expansion of harmonic mean of Pi and e.

Original entry on oeis.org

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

Views

Author

Zak Seidov, Oct 05 2002

Keywords

Examples

			2.91464748906626618...

Crossrefs

Cf. A000796 (Pi), A001113 (e), A074916, A074917, A074921.

Programs

  • Mathematica
    RealDigits[HarmonicMean[{Pi,E}],10,120][[1]] (* Harvey P. Dale, Jul 05 2020 *)
  • PARI
    2/(1/Pi + 1/exp(1)) \\ Michel Marcus, Oct 03 2013

Formula

Equals 2/(1/Pi + 1/e).

A074917 Decimal expansion of (Pi+e)/2 - decimal expansion of (Pi*e)^(1/2).

Original entry on oeis.org

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

Views

Author

Zak Seidov, Oct 01 2002

Keywords

Crossrefs

Cf. A019645, A074916, A074921.

Programs

  • Mathematica
    RealDigits[(Pi+E)/2,10,120][[1]]-RealDigits[Sqrt[Pi E],10,120][[1]] (* Harvey P. Dale, Sep 05 2023 *)

A177910 2 log_10 ((e + Pi)/2).

Original entry on oeis.org

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

Views

Author

Alonso del Arte, Dec 15 2010

Keywords

Examples

			0.9337166358149140117514...

References

  • Jonathan Borwein & Peter Borwein, A Dictionary of Real Numbers. Pacific Grove, California: Wadsworth & Brooks/Cole Advanced Books & Software (1990) p. iii, p. 396
  • Ian H. Witten, Alistair Moffat, Timothy C. Bell, Managing Gigabytes: Compressing and Indexing Documents and Images, San Francisco: Morgan Kaufmann (1999): p. 11

Crossrefs

Cf. A074916 ((e + Pi)/2).

Programs

  • Mathematica
    RealDigits[N[2Log[10, (E + Pi)/2], 105]][[1]]
  • PARI
    2*log((exp(1)+Pi)/2)/log(10) \\ Michel Marcus, Mar 14 2015

A342209 Decimal expansion of logarithmic mean of Pi and e.

Original entry on oeis.org

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

Views

Author

Gleb Koloskov, Mar 05 2021

Keywords

Comments

The logarithmic mean of Pi and e lies between the arithmetic and geometric means of Pi and e.

Examples

			2.9248335452376948992733592...

Links

Crossrefs

Cf. A000796 (Pi), A001113 (e), A019645, A074916, A074948, A074950, A074957.

Programs

  • Mathematica
    RealDigits[(Pi - E)/(Log[Pi] - 1), 10, 100][[1]] (* Amiram Eldar, Mar 06 2021 *)
  • PARI
    (Pi-exp(1))/(log(Pi)-1)

Formula

Equals (Pi-e)/(log(Pi)-1).
Showing 1-6 of 6 results.

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