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A272876
Decimal expansion of the imaginary part of the infinite nested power (1+(1+(1+...)^i)^i)^i, with i being the imaginary unit.
6
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
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
KEYWORD
nonn,cons
AUTHOR
Stanislav Sykora, May 15 2016
STATUS
approved