A305202 -id:A305202 - cp's OEIS frontend

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

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

Keerthi Vasan Gopala, May 27 2018

			0.576412723031435283148289239887068476278...

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

Eric Weisstein's World of Mathematics, Lambert W-Function
Wikipedia, Lambert W function

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

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 *)

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)

More digits from Alois P. Heinz, May 27 2018

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

Keerthi Vasan Gopala, May 27 2018

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

			0.88530292263172060173561116234106499518957753397967...

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

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

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

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

Keerthi Vasan Gopala, May 27 2018

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

			0.256299537163861312529996729880982538078341463884...

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

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

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

cp's OEIS Frontend

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

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

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

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