

A290409


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


3



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

0,1


COMMENTS

In C, the unique invariant point of the mapping M(z) = (i+z)^i is also its attractor. The convergence is linear and takes about 1650 iterations to reduce the value of z  M(z) by 1000 decimal digits. The imaginary part of the invariant point is in A290410.
Considering the definition, one can symbolically write A290409 + i*A290410 = (i+(i+(i+...)^i)^i)^i.


LINKS

Stanislav Sykora, Table of n, a(n) for n = 0..2000
Eric Weisstein's World of Mathematics, Complex Exponentiation


EXAMPLE

0.269293437169311227190868021268862010532911006037684671712716015...


PROG

(PARI) \p 3000 \\ Set precision
M(z)=(z+I)^I; \\ Mapping M
z=1.0; for(k=1, 2000, z=M(z)); \\ Initialize and iterate
d = floor(log(abs(zM(z)))/log(10)) \\ A crude convergence test
real(z) \\ The result; keep << d digits, and test for stability.


CROSSREFS

Cf. A272875, A272876, A272877, A290408, A290410.
Sequence in context: A129635 A231985 A205527 * A269558 A195396 A197579
Adjacent sequences: A290406 A290407 A290408 * A290410 A290411 A290412


KEYWORD

nonn,cons


AUTHOR

Stanislav Sykora, Jul 30 2017


STATUS

approved



