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

Author

Keerthi Vasan Gopala, May 27 2018

Keywords

• nonn
• cons

Examples

			0.576412723031435283148289239887068476278...
		

References

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

Links

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

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