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

Author

Stanislav Sykora, May 15 2016

Keywords

• nonn
• cons

Comments

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

Examples

			0.40756393054562184473966324339415208864062799286677510304874835...
		

Links

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

Crossrefs

Cf. A156590, A272875, A272877.

Programs

Mathematica

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

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)