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.

A231736 Decimal expansion of the natural logarithm of Pi^Pi.

Original entry on oeis.org

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

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Author

Stanislav Sykora, Nov 13 2013

Keywords

Examples

			3.59627499972915819808600175164636038136917928975387723049724412082...

Links

Crossrefs

Cf. A000796, A053510, A073233, A231737.

Programs

  • Mathematica
    RealDigits[Pi * Log[Pi], 10, 120][[1]] (* Amiram Eldar, May 17 2023 *)
  • PARI
    Pi*log(Pi)

Formula

Equals Pi*log(Pi).

A236100 Decimal expansion of the real part of Pi^(I/Pi).

Original entry on oeis.org

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

Views

Author

Stanislav Sykora, Jan 19 2014

Keywords

Comments

The imaginary part is in A236101.

Examples

			0.9343453036786376942622408604544211862401851213899337514...

Links

Crossrefs

Cf. A000796, A053510, A073233, A231736, A236101, A236098, A236099.

Programs

  • Mathematica
    RealDigits[Re[Pi^(I/Pi)],10,120][[1]] (* Harvey P. Dale, Aug 02 2017 *)

Formula

real(Pi^(I/Pi)) = cos(log(Pi)/Pi) = cos(A231737).

A236101 Decimal expansion of the imaginary part of Pi^(i/Pi).

Original entry on oeis.org

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

Views

Author

Stanislav Sykora, Jan 19 2014

Keywords

Comments

The real part is in A236100.

Examples

			0.35636898503331389990769183737865940578845872790065930829963...

Links

Crossrefs

Cf. A000796, A053510, A073233, A231736, A236100, A236098, A236099.

Programs

  • Mathematica
    RealDigits[Sin[Log[Pi]/Pi], 10, 120][[1]] (* Amiram Eldar, Jun 06 2023 *)

Formula

Equals imag(Pi^(i/Pi)) = sin(log(Pi)/Pi) = sin(A231737).

A348261 Decimal expansion of the nontrivial number x for which x^Pi = Pi^x.

Original entry on oeis.org

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

Views

Author

Timothy L. Tiffin, Oct 08 2021

Keywords

Comments

The x-th root of x equals the Pi-th root of Pi: x^(1/x) = Pi^(1/Pi) = A073238 = 1.43961949584759... .
Like Pi, is x also transcendental?

Examples

			2.382179087993018774555593052520878...
x^Pi = Pi^x = 15.28621734783496640312486439999472... .

Crossrefs

Cf. A000796 (Pi), A049541 (1/Pi), A073238 (Pi^(1/Pi)), A073226 (e^e, see first comment), A231737.

Programs

  • Maple
    evalf((t-> -LambertW(-t)/t)(log(Pi)/Pi), 120);  # Alois P. Heinz, Oct 13 2021
  • Mathematica
    {a, b} = NSolve[x^Pi == Pi^x, x, WorkingPrecision -> 300]; a; RealDigits[N[x/.a, 300]][[1]]

Formula

Equals -Pi*LambertW(-log(Pi)/Pi)/log(Pi). - Alois P. Heinz, Oct 13 2021
Showing 1-4 of 4 results.

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