The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A290409 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A290409

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

#20 by Michel Marcus at Tue May 30 02:20:15 EDT 2023

STATUS

reviewed

approved

#19 by Joerg Arndt at Tue May 30 01:32:44 EDT 2023

STATUS

proposed

reviewed

#18 by Amiram Eldar at Tue May 30 01:02:50 EDT 2023

STATUS

editing

proposed

#17 by Amiram Eldar at Tue May 30 00:24:52 EDT 2023

LINKS

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ComplexExponentiation.html">Complex Exponentiation</a>.

MATHEMATICA

RealDigits[Re[z /. FindRoot[(I + z)^I == z, {z, 0}, WorkingPrecision -> 120]]][[1]] (* Amiram Eldar, May 30 2023 *)

STATUS

approved

editing

#16 by N. J. A. Sloane at Fri Aug 18 19:12:02 EDT 2017

STATUS

proposed

approved

#15 by Michel Marcus at Fri Aug 04 06:52:37 EDT 2017

STATUS

editing

proposed

Discussion

Fri Aug 04

06:53

Michel Marcus: ok ?

07:59

Stanislav Sykora: sure

#14 by Michel Marcus at Fri Aug 04 06:52:29 EDT 2017

LINKS

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ComplexExponentiation.html">Complex Exponentiation</a>

STATUS

proposed

editing

#13 by Jon E. Schoenfield at Wed Aug 02 21:26:43 EDT 2017

STATUS

editing

proposed

#12 by Jon E. Schoenfield at Wed Aug 02 21:26:37 EDT 2017

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.

STATUS

proposed

editing

#11 by Stanislav Sykora at Mon Jul 31 04:18:01 EDT 2017

STATUS

editing

proposed

Discussion

Mon Jul 31

05:31

Joerg Arndt: Pari has a function "solve", suggest to use it.

06:11

Stanislav Sykora: Solve for complex? PARI says "solve(X = a; b; expr). Find a real root of expression expr between a and b". Besides, I find attractors more interesting than mere solving :-(