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

0,1

References

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

Links

Table of n, a(n) for n=0..105.

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

Wikipedia, Lambert W function

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)

Example

0.576412723031435283148289239887068476278...

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 *)

Crossrefs

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

Sequence in context: A175294 A196615 A374967 * A198730 A318733 A195444

Adjacent sequences: A305197 A305198 A305199 * A305201 A305202 A305203

Keyword

nonn,cons

Author

Keerthi Vasan Gopala, May 27 2018

Extensions

More digits from Alois P. Heinz, May 27 2018

Status

approved