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A104748
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Decimal expansion of solution to x*2^x=1.
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6
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6, 4, 1, 1, 8, 5, 7, 4, 4, 5, 0, 4, 9, 8, 5, 9, 8, 4, 4, 8, 6, 2, 0, 0, 4, 8, 2, 1, 1, 4, 8, 2, 3, 6, 6, 6, 5, 6, 2, 8, 2, 0, 9, 5, 7, 1, 9, 1, 1, 0, 1, 7, 5, 5, 1, 3, 9, 6, 9, 8, 7, 9, 7, 5, 4, 3, 4, 8, 7, 4, 9, 1, 8, 7, 8, 7, 9, 9, 7, 6, 2, 2, 3, 4, 0, 5, 3, 6, 9, 3, 4, 9, 9, 1, 6, 8, 5, 8, 8, 5, 9, 2, 3, 3, 3
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Writing the equation as (1/2)^x = x, the solution is the value of the infinite power tower function h(t) = t^t^t^... at t = 1/2. The solution is a transcendental number. [Jonathan Sondow, Aug 29 2011]
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LINKS
| J. Sondow and D. Marques, Algebraic and transcendental solutions of some exponential equations, Annales Mathematicae et Informaticae 37 (2010) 151-164; see p. 160.
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EXAMPLE
| x = 0.641185744504985984486200482114823666562820957191101... = (1/2)^(1/2)^(1/2)^...
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MATHEMATICA
| RealDigits[ ProductLog[ Log[2]]/Log[2], 10, 111][[1]] (from Robert G. Wilson v Mar 23 2005)
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CROSSREFS
| Equals 1/A030798.
Cf. A073084.
Sequence in context: A060780 A199391 A106333 * A117335 A021863 A190405
Adjacent sequences: A104745 A104746 A104747 * A104749 A104750 A104751
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KEYWORD
| nonn,cons
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AUTHOR
| Zak Seidov (zakseidov(AT)yahoo.com), Mar 23 2005
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 23 2005
Offset corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 05 2009
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