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 A059527 Decimal expansion of imaginary part of solution to z = log z. 9
 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 (list; constant; graph; refs; listen; history; text; internal format)
 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

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Last modified September 13 07:46 EDT 2024. Contains 375880 sequences. (Running on oeis4.)