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%I A272876 #9 May 26 2023 05:42:49
%S A272876 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,
%T A272876 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,
%U A272876 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
%N A272876 Decimal expansion of the imaginary part of the infinite nested power (1+(1+(1+...)^i)^i)^i, with i being the imaginary unit.
%C A272876 The real part and the modulus of this complex constant are in A272875 and A272877, respectively. For more information, see A272875.
%H A272876 Stanislav Sykora, <a href="/A272876/b272876.txt">Table of n, a(n) for n = 0..2000</a>
%e A272876 0.40756393054562184473966324339415208864062799286677510304874835...
%t A272876 RealDigits[Im[z /. FindRoot[(1 + z)^I == z, {z, 0}, WorkingPrecision -> 120]]][[1]] (* _Amiram Eldar_, May 26 2023 *)
%o A272876 (PARI) \\ f(x) computes (x+(x+...)^i)^i, provided that it converges:
%o A272876 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)}
%o A272876 \\ To compute this constant, use:
%o A272876 z0 = f(1); imag(z0)
%Y A272876 Cf. A156590, A272875, A272877.
%K A272876 nonn,cons
%O A272876 0,1
%A A272876 _Stanislav Sykora_, May 15 2016

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