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A059526
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Decimal expansion of real part of solution to z = log z.
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1
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3, 1, 8, 1, 3, 1, 5, 0, 5, 2, 0, 4, 7, 6, 4, 1, 3, 5, 3, 1, 2, 6, 5, 4, 2, 5, 1, 5, 8, 7, 6, 6, 4, 5, 1, 7, 2, 0, 3, 5, 1, 7, 6, 1, 3, 8, 7, 1, 3, 9, 9, 8, 6, 6, 9, 2, 2, 3, 7, 8, 6, 0, 6, 2, 2, 9, 4, 1, 3, 8, 7, 1, 5, 5, 7, 6, 2, 6, 9, 7, 9, 2, 3, 2, 4, 8, 6, 3, 8, 4, 8, 9, 8, 6, 3, 6, 1, 6, 3, 8, 4, 4, 2, 1, 4
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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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.
A complex number w with a negative imaginary part will converge to the conjugate of z since log(conjugate(w)) = conjugate(log(w)). [From Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), Mar 02 2009]
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REFERENCES
| Wolfram Research, Mathematica, Version 4.1.0.0, Help Browser, under the function FixedPoint.
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EXAMPLE
| z = 0.31813150520476413531265425158766451720351761387139986692237... + 1.33723570143068940890116214319371061253950213846051241887631... *iI
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MATHEMATICA
| RealDigits[ Re[ N[ FixedPoint[ Log, 1 + I, 910], 105]]] [[1]]
RealDigits[ N[ Re[ ProductLog[-1]], 105]][[1]] (* From Jean-François Alcover, Feb 01 2012 *)
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CROSSREFS
| Imaginary part is A059527.
Sequence in context: A165498 A195731 A154294 * A091839 A155789 A179393
Adjacent sequences: A059523 A059524 A059525 * A059527 A059528 A059529
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KEYWORD
| cons,nonn,nice,changed
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AUTHOR
| Fabian Rothelius (fabian.rothelius(AT)telia.com), Jan 21 2001
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 26 2001
Edited and extended by Robert G. Wilson v (kspaint.com), Aug 22 2002
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