A272876 Decimal expansion of the imaginary part of the infinite nested power (1+(1+(1+...)^i)^i)^i, with i being the imaginary unit.

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

Offset

0,1

Comments

The real part and the modulus of this complex constant are in A272875 and A272877, respectively. For more information, see A272875.

Links

Stanislav Sykora, Table of n, a(n) for n = 0..2000

Example

0.40756393054562184473966324339415208864062799286677510304874835...

Mathematica

RealDigits[Im[z /. FindRoot[(1 + z)^I == z, {z, 0}, WorkingPrecision -> 120]]][[1]] (* Amiram Eldar, May 26 2023 *)

Prog

(PARI) \\ f(x) computes (x+(x+...)^i)^i, provided that it converges:
f(x)={my(z=1.0, zlast=0.0, eps=10.0^(1-default(realprecision))); while(abs(z-zlast)>eps, zlast=z; z=(x+z)^I); return(z)}
\\ To compute this constant, use:
z0 = f(1); imag(z0)

Crossrefs

Cf. A156590, A272875, A272877.

Sequence in context: A057641 A352886 A336029 * A133930 A077892 A117543

Adjacent sequences: A272873 A272874 A272875 * A272877 A272878 A272879

Keyword

nonn,cons

Author

Stanislav Sykora, May 15 2016

Status

approved