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%I #14 May 30 2023 02:19:56
%S 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,
%T 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,
%U 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
%N Decimal expansion of the imaginary part of the solution of z = (i+z)^i in C (i is the imaginary unit).
%C For more comments, see the real part in A290409.
%H Stanislav Sykora, <a href="/A290410/b290410.txt">Table of n, a(n) for n = -1..2000</a>
%e 0.012576454573863832381561850841183677014423243473407635203417674...
%t RealDigits[Im[z /. FindRoot[(I + z)^I == z, {z, 0}, WorkingPrecision -> 120]]][[1]] (* _Amiram Eldar_, May 30 2023 *)
%o (PARI) \p 3000 \\ Set precision
%o M(z)=(z+I)^I; \\ Mapping M
%o z=1.0;for(k=1,2000,z=M(z)); \\ Initialize and iterate
%o d = -floor(log(abs(z-M(z)))/log(10)) \\ A crude convergence test
%o imag(z) \\ The result; keep << d digits, and test for stability.
%Y Cf. A272875, A272876, A272877, A290408, A290409.
%K nonn,cons
%O -1,2
%A _Stanislav Sykora_, Jul 30 2017
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