login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; constant; graph; refs; listen; history; text; internal format)
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 1e-3400. 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(z-Mp(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: A010610 A140059 A070517 * A028232 A225359 A060310

Adjacent sequences:  A290405 A290406 A290407 * A290409 A290410 A290411

KEYWORD

nonn,cons

AUTHOR

Stanislav Sykora, Jul 30 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified September 26 10:52 EDT 2017. Contains 292518 sequences.