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.

A277522 Decimal expansion of the first derivative of the infinite power tower function x^x^x... at x = 1/2.

Original entry on oeis.org

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

Views

Author

Alois P. Heinz, Oct 19 2016

Keywords

Examples

			0.5692452044263480610653304778419669052638659731463...

Links

Crossrefs

Cf. A033917, A104748, A277523, A277524, A277525, A277526, A277527, A277528, A277529, A277530, A277531, A277559, A277651, A293009, A300916.

Programs

  • Mathematica
    RealDigits[2 Exp[-2 ProductLog[Log[2]]]/(1 + ProductLog[Log[2]]), 10, 105][[1]] (* Vladimir Reshetnikov, Oct 20 2016 *)
f[x_] := -ProductLog[-Log[x]]/Log[x]; RealDigits[f'[1/2], 10, 120][[1]] (* Amiram Eldar, May 23 2023 *)
  • PARI
    2*exp(-2*lambertw(log(2)))/(1+lambertw(log(2))) \\ G. C. Greubel, Nov 10 2017

Formula

Equals 2*exp(-2*LambertW(log(2)))/(1+LambertW(log(2))). - Vladimir Reshetnikov, Oct 20 2016

A293009 Decimal expansion of the first derivative of the infinite power tower function x^x^x... at x = 1/Pi.

Original entry on oeis.org

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

Views

Author

Alois P. Heinz, Mar 16 2018

Keywords

Examples

			0.56501844596024150528994096062245192028392680078511838285519...

Links

Crossrefs

Cf. A000796, A049541, A073243, A277522, A277651, A300916.

Programs

  • Mathematica
    RealDigits[Pi*Exp[-2*LambertW[Log[Pi]]]/(1+LambertW[Log[Pi]]), 10, 100][[1]] (* G. C. Greubel, Sep 09 2018 *)
  • PARI
    Pi*exp(-2*lambertw(log(Pi)))/(1+lambertw(log(Pi))) \\ Michel Marcus, Mar 16 2018

Formula

Equals Pi*exp(-2*LambertW(log(Pi)))/(1+LambertW(log(Pi))).

A300916 Decimal expansion of the first derivative of the infinite power tower function x^x^x... at x = 1/e.

Original entry on oeis.org

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

Views

Author

Alois P. Heinz, Mar 16 2018

Keywords

Examples

			0.557919282255416046773864733137284325268059522147000568856861678665669168...

Links

Crossrefs

Cf. A001113, A030178, A068985, A277522, A277651, A293009.

Programs

  • Mathematica
    RealDigits[E*Exp[-2*LambertW[1]]/(1+LambertW[1]), 10, 100][[1]] (* G. C. Greubel, Sep 09 2018 *)
  • PARI
    exp(1)*exp(-2*lambertw(1))/(1+lambertw(1)) \\ Michel Marcus, Mar 16 2018

Formula

Equals exp(1)*exp(-2*LambertW(1))/(1+LambertW(1)).

A277559 Decimal expansion of the first derivative of the infinite power tower function x^x^x... at x = sqrt(2).

Original entry on oeis.org

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

Views

Author

Alois P. Heinz, Oct 19 2016

Keywords

Comments

It is known that sqrt(2)^sqrt(2)^sqrt(2)^... = 2.

Examples

			9.21753670019231544705131363265247919608239799603795429...

Links

Crossrefs

Cf. A002162, A002193, A010466, A244009, A277522, A277651.

Programs

  • Magma
    Sqrt(8)/(1-Log(2)); // G. C. Greubel, Jul 27 2018
  • Mathematica
    RealDigits[Sqrt[8]/(1-Log[2]), 10, 100][[1]] (* G. C. Greubel, Jul 27 2018 *)
  • PARI
    sqrt(8)/(1-log(2)) \\ Michel Marcus, Oct 20 2016

Formula

Equals 2^(3/2)/(1-log(2)).
Equals A010466/A244009. - Michel Marcus, Oct 20 2016
Showing 1-4 of 4 results.

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