A330392 Decimal expansion of smallest x > 1 satisfying x^(i*x) = 1, where i is the imaginary unit.

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

Offset

1,1

Links

Table of n, a(n) for n=1..105.

Tim Warriner, Removing the Mystery of Euler’s Formula exp(iθ) = cos θ + i sin θ.

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

Wikipedia, Lambert W function.

Formula

Equals 1/A202495.

Equals 2*Pi/LambertW(2*Pi). - Alois P. Heinz, Feb 26 2020

Example

4.3045303245174394156571018783220431826714954589838...

Maple

evalf(2*Pi/LambertW(2*Pi), 145);  # Alois P. Heinz, Feb 26 2020

Mathematica

RealDigits[(2*Pi)/ProductLog[2*Pi], 10, 120][[1]] (* Amiram Eldar, May 31 2023 *)

Prog

(PARI) 2*Pi/lambertw(2*Pi) \\ Michel Marcus, Feb 27 2020

Crossrefs

Cf. A000796, A202495.

Sequence in context: A267410 A016697 A086466 * A204694 A304030 A338802

Adjacent sequences: A330389 A330390 A330391 * A330393 A330394 A330395

Keyword

nonn,cons

Author

Tim Warriner, Feb 26 2020

Status

approved