A290410 Decimal expansion of the imaginary part of the solution of z = (i+z)^i in C (i is the imaginary unit).

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

Offset

-1,2

Comments

For more comments, see the real part in A290409.

Links

Stanislav Sykora, Table of n, a(n) for n = -1..2000

Example

0.012576454573863832381561850841183677014423243473407635203417674...

Mathematica

RealDigits[Im[z /. FindRoot[(I + z)^I == z, {z, 0}, WorkingPrecision -> 120]]][[1]] (* Amiram Eldar, May 30 2023 *)

Prog

(PARI) \p 3000 \\ Set precision
M(z)=(z+I)^I; \\ Mapping M
z=1.0; for(k=1, 2000, z=M(z)); \\ Initialize and iterate
d = -floor(log(abs(z-M(z)))/log(10)) \\ A crude convergence test
imag(z) \\ The result; keep << d digits, and test for stability.

Crossrefs

Cf. A272875, A272876, A272877, A290408, A290409.

Sequence in context: A257963 A167554 A202392 * A078320 A306992 A325437

Adjacent sequences: A290407 A290408 A290409 * A290411 A290412 A290413

Keyword

nonn,cons

Author

Stanislav Sykora, Jul 30 2017

Status

approved