A059527 Decimal expansion of imaginary part of solution to z = log z.

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

Offset

1,2

Comments

Repeatedly take logs, starting from any number not equal to 0, 1, e, e^e, e^(e^e), etc. and you will converge to 0.31813150... + 1.33723570...*I.

Links

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

Stanislav Sykora, Fixed points of the mappings exp(z) and -exp(z) in C, 2016.

Wolfram Research, FixedPoint

Example

z = 0.31813150520476413531265425158766451720351761387139986692237... + 1.33723570143068940890116214319371061253950213846051241887631... *i.

Mathematica

RealDigits[ Im[ N[ FixedPoint[ Log, 1 + I, 910], 105]]] [[1]]
RealDigits[ N[ Im[ ProductLog[-1]], 105]][[1]] (* Jean-François Alcover, Feb 01 2012 *)

Prog

(PARI) z=I; for(k=1, 16000, z=log(z)); imag(z)  \\ Using realprecision \p 2010. - Stanislav Sykora, Jun 07 2015
(PARI) z=I; for(k=1, 10, z-=(z-log(z))/(1-1/z)); imag(z) \\ Jeremy Tan, Sep 23 2017

Crossrefs

Real part is A059526.

Cf. A030178.

Sequence in context: A359407 A358191 A235162 * A215235 A101457 A280753

Adjacent sequences: A059524 A059525 A059526 * A059528 A059529 A059530

Keyword

cons,nonn,nice

Author

Fabian Rothelius, Jan 21 2001

Extensions

More terms from Vladeta Jovovic, Feb 26 2001

Edited and extended by Robert G. Wilson v, Aug 22 2002

Status

approved