

A290408


Decimal expansion of the real part of the solution of z = (i+z)^(i) in C (i is the imaginary unit).


3



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

1,2


COMMENTS

In C, the unique invariant point of the mapping M(z) = (i+z)^(i) is not the attractor of the mapping (unstable behavior), but it is an attractor of the modified mapping M'(z) = (z+M(z))/2. For M', it takes 5000 iterations to reduce the value of z  M'(z) below 1e3400. Interestingly, the imaginary part of z seems to be equal to 1/2 (verified to 5000 digits). If this conjecture holds, and considering the definition, one can symbolically write (i+(i+(i+...)^(i))^(i))^(i) = a  i/2.


LINKS

Stanislav Sykora, Table of n, a(n) for n = 1..2000


EXAMPLE

1.3392091685291119683592699857627641708859882632690433847739675808721...


PROG

(PARI) \p 4000 \\ Set precision
Mp(z)=0.5*(z+I)^(I); \\ Mapping M'
z=1.0; for(k=1, 5000, z=Mp(z)); \\ Initialize and iterate
d = floor(log(abs(zMp(z)))/log(10)) \\ Crude convergence test (3438)
real(z) \\ The result; keep << d digits, and test for stability.


CROSSREFS

Cf. A272875, A272876, A272877, A290409, A290410.
Sequence in context: A140059 A324895 A070517 * A028232 A225359 A060310
Adjacent sequences: A290405 A290406 A290407 * A290409 A290410 A290411


KEYWORD

nonn,cons


AUTHOR

Stanislav Sykora, Jul 30 2017


STATUS

approved



