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 1-9 of 9 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

A277523 Decimal expansion of the second derivative of the infinite power tower function x^x^x... at x = 1/2.

Original entry on oeis.org

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

Views

Author

Alois P. Heinz, Oct 19 2016

Keywords

Examples

			0.222140213601222126551553738596800308959108972686281...

Links

Crossrefs

Cf. A033917, A104748 (0th derivative), A277522, A277524, A277525, A277526, A277527, A277528, A277529, A277530, A277531.

Programs

  • Mathematica
    RealDigits[4 LambertW[Log[2]]^2 ((2 - Log[2]) LambertW[Log[2]]^2 + (3 - 2 Log[2]) LambertW[Log[2]] - Log[2])/(Log[2] (1 + LambertW[Log[2]]))^3, 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
    4*lambertw(log(2))^2*((2-log(2))*lambertw(log(2))^2 + (3-2*log(2)) *lambertw(log(2))-log(2))/(log(2)*(1+lambertw(log(2))))^3 \\ G. C. Greubel, Nov 10 2017

Formula

Equals 4 * LambertW(log(2))^2 * ((2-log(2)) * LambertW(log(2))^2 + (3-2*log(2)) * LambertW(log(2))-log(2)) / (log(2) * (1+LambertW(log(2))))^3. - Vladimir Reshetnikov, Oct 20 2016

A277524 Decimal expansion of the third derivative of the infinite power tower function x^x^x... at x = 1/2.

Original entry on oeis.org

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

Views

Author

Alois P. Heinz, Oct 19 2016

Keywords

Examples

			1.901713907526003986262639982124699514446488574524050...

Links

Crossrefs

Cf. A033917, A104748, A277522, A277523, A277525, A277526, A277527, A277528, A277529, A277530, A277531.

Programs

  • Mathematica
    f[x_] := -ProductLog[-Log[x]]/Log[x]; RealDigits[f'''[1/2], 10, 120][[1]] (* Amiram Eldar, May 23 2023 *)

A277525 Decimal expansion of the fourth derivative of the infinite power tower function x^x^x... at x = 1/2, negated.

Original entry on oeis.org

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

Views

Author

Alois P. Heinz, Oct 19 2016

Keywords

Examples

			-1.7296376776755434144759943668608340411378592485876...

Links

Crossrefs

Cf. A033917, A104748, A277522, A277523, A277524, A277526, A277527, A277528, A277529, A277530, A277531.

Programs

  • Mathematica
    f[x_] := -ProductLog[-Log[x]]/Log[x]; RealDigits[Derivative[4][f][1/2], 10, 120][[1]] (* Amiram Eldar, May 23 2023 *)

A277526 Decimal expansion of the fifth derivative of the infinite power tower function x^x^x... at x = 1/2.

Original entry on oeis.org

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

Views

Author

Alois P. Heinz, Oct 19 2016

Keywords

Examples

			49.2859076375851017760335178789285712579571478...

Links

Crossrefs

Cf. A033917, A104748, A277522, A277523, A277524, A277525, A277527, A277528, A277529, A277530, A277531.

Programs

  • Mathematica
    f[x_] := -ProductLog[-Log[x]]/Log[x]; RealDigits[Derivative[5][f][1/2], 10, 120][[1]] (* Amiram Eldar, May 23 2023 *)

A277527 Decimal expansion of the sixth derivative of the infinite power tower function x^x^x... at x = 1/2, negated.

Original entry on oeis.org

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

Views

Author

Alois P. Heinz, Oct 19 2016

Keywords

Examples

			-277.441320354061791058569551395984751488030915...

Links

Crossrefs

Cf. A033917, A104748, A277522, A277523, A277524, A277525, A277526, A277528, A277529, A277530, A277531.

Programs

  • Mathematica
    f[x_] := -ProductLog[-Log[x]]/Log[x]; RealDigits[Derivative[6][f][1/2], 10, 120][[1]] (* Amiram Eldar, May 23 2023 *)

A277528 Decimal expansion of the seventh derivative of the infinite power tower function x^x^x... at x = 1/2.

Original entry on oeis.org

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

Views

Author

Alois P. Heinz, Oct 19 2016

Keywords

Examples

			4349.0288567288378480022252140838951499169615339...

Links

Crossrefs

Cf. A033917, A104748, A277522, A277523, A277524, A277525, A277526, A277527, A277529, A277530, A277531.

Programs

  • Mathematica
    f[x_] := -ProductLog[-Log[x]]/Log[x]; RealDigits[Derivative[7][f][1/2], 10, 120][[1]] (* Amiram Eldar, May 23 2023 *)

A277529 Decimal expansion of the eighth derivative of the infinite power tower function x^x^x... at x = 1/2, negated.

Original entry on oeis.org

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

Views

Author

Alois P. Heinz, Oct 19 2016

Keywords

Examples

			-50109.2762750366968958680172353229451272183942...

Links

Crossrefs

Cf. A033917, A104748, A277522, A277523, A277524, A277525, A277526, A277527, A277528, A277530, A277531.

Programs

  • Mathematica
    f[x_] := -ProductLog[-Log[x]]/Log[x]; RealDigits[Derivative[8][f][1/2], 10, 120][[1]] (* Amiram Eldar, May 23 2023 *)

A277530 Decimal expansion of the ninth derivative of the infinite power tower function x^x^x... at x = 1/2.

Original entry on oeis.org

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

Views

Author

Alois P. Heinz, Oct 19 2016

Keywords

Examples

			844617.08671093611975158207114938322395461002...

Links

Crossrefs

Cf. A033917, A104748, A277522, A277523, A277524, A277525, A277526, A277527, A277528, A277529, A277531.

Programs

  • Mathematica
    f[x_] := -ProductLog[-Log[x]]/Log[x]; RealDigits[Derivative[9][f][1/2], 10, 120][[1]] (* Amiram Eldar, May 23 2023 *)
Showing 1-9 of 9 results.

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