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
Examples
4.3045303245174394156571018783220431826714954589838...
Links
- 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.
Programs
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Maple
evalf(2*Pi/LambertW(2*Pi), 145); # Alois P. Heinz, Feb 26 2020
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Mathematica
RealDigits[(2*Pi)/ProductLog[2*Pi], 10, 120][[1]] (* Amiram Eldar, May 31 2023 *)
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PARI
2*Pi/lambertw(2*Pi) \\ Michel Marcus, Feb 27 2020
Formula
Equals 1/A202495.
Equals 2*Pi/LambertW(2*Pi). - Alois P. Heinz, Feb 26 2020