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.

User: Keerthi Vasan Gopala

Keerthi Vasan Gopala's wiki page.

Keerthi Vasan Gopala has authored 4 sequences.

A305210 Decimal expansion of the imaginary part of continued exponential (i/Pi).

Original entry on oeis.org

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

Views

Author

Keerthi Vasan Gopala, May 27 2018

Keywords

Comments

This is the imaginary part of e^((i/Pi)*e^((i/Pi)*e^((i/Pi)...))).

Examples

			0.256299537163861312529996729880982538078341463884...

Crossrefs

Cf. A049006, A077589, A077590, A305200, A305202, A305208.

Programs

  • Mathematica
    Im[Pi*I*N[ProductLog[-I/Pi], 100]]

Formula

Equals Im(Pi*i*LambertW(-i/Pi)).

A305208 Decimal expansion of the real part of the continued exponential i/Pi.

Original entry on oeis.org

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

Views

Author

Keerthi Vasan Gopala, May 27 2018

Keywords

Comments

This is the real part of e^((i/Pi)*e^((i/Pi)*e^((i/Pi)...))).

Examples

			0.88530292263172060173561116234106499518957753397967...

Crossrefs

Cf. A049006, A077589, A077590, A305200, A305202, A305210.

Programs

  • Mathematica
    Re[Pi*I*N[ProductLog[-I/Pi], 100]]

Formula

Equals Re(Pi*i*LambertW(-i/Pi)).

A305202 Decimal expansion of the imaginary part of continued exponential i.

Original entry on oeis.org

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

Views

Author

Keerthi Vasan Gopala, May 27 2018

Keywords

Comments

This is the imaginary part of e^(i*e^(i*e^(i...))).

Examples

			0.3746990207371174936059784287597208075128...

Links

Crossrefs

Cf. A305200.

Programs

  • Mathematica
    RealDigits[Re[LambertW[I]], 10, 120][[1]] (* Vaclav Kotesovec, Oct 02 2021 *)

Formula

Equals Im(i*LambertW(-i)). - Alois P. Heinz, May 27 2018
Equals Re(LambertW(i)). - Vaclav Kotesovec, Oct 02 2021

Extensions

More digits from Alois P. Heinz, May 27 2018

A305200 Decimal expansion of the real part of continued exponential of i.

Original entry on oeis.org

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

Views

Author

Keerthi Vasan Gopala, May 27 2018

Keywords

Examples

			0.576412723031435283148289239887068476278...

References

  • This is the real part of e^(i*e^(i*e^(i...))).

Links

Crossrefs

Cf. A049006, A077589, A077590, A191719, A305202.

Programs

  • Mathematica
    RealDigits[Re[I*LambertW[-I]],10,120][[1]] (* Harvey P. Dale, Dec 01 2018 *)
RealDigits[x /. FindRoot[E^(x*Tan[x]) == Cos[x]/x, {x, 1/2}, WorkingPrecision -> 120]][[1]] (* Vaclav Kotesovec, Oct 02 2021 *)

Formula

Equals Re(i*LambertW(-i)). - Alois P. Heinz, May 27 2018
From Vaclav Kotesovec, Oct 02 2021: (Start)
Root of the equation exp(x*tan(x)) = cos(x)/x.
Equals Im(LambertW(i)). (End)

Extensions

More digits from Alois P. Heinz, May 27 2018

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