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Search: id:A059526
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| A059526 |
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Decimal expansion of real part of solution to z = log z. |
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+0
2
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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; cons; graph; listen)
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OFFSET
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0,1
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COMMENT
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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
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Wolfram Research, Mathematica, Version 4.1.0.0, Help Browser, under the function FixedPoint.
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EXAMPLE
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z = 0.31813150520476413531265425158766451720351761387139986692237... + 1.33723570143068940890116214319371061253950213846051241887631... *iI
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MATHEMATICA
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RealDigits[ Re[ N[ FixedPoint[ Log, 1 + I, 910], 125]]] [[1]]
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CROSSREFS
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Imaginary part is A059527.
Sequence in context: A141252 A165498 A154294 this_sequence A091839 A155789 A112420
Adjacent sequences: A059523 A059524 A059525 this_sequence A059527 A059528 A059529
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KEYWORD
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cons,nonn,nice
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AUTHOR
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Fabian Rothelius (fabian.rothelius(AT)telia.com), Jan 21 2001
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EXTENSIONS
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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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