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 A104748 Decimal expansion of solution to x*2^x = 1. 18
 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; text; internal format)
 OFFSET 0,1 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 Equals LambertW(log(2))/log(2) since, for 1/E^E <= c < 1, c^c^c^...= LambertW(log(1/c))/log(1/c). - Stanislav Sykora, Nov 03 2013 LINKS Stanislav Sykora, Table of n, a(n) for n = 0..2000 J. Sondow and D. Marques, Algebraic and transcendental solutions of some exponential equations, Annales Mathematicae et Informaticae 37 (2010) 151-164; see p. 160. Wikipedia, Lambert W function EXAMPLE x = 0.641185744504985984486200482114823666562820957191101... = (1/2)^(1/2)^(1/2)^... MATHEMATICA RealDigits[ ProductLog[ Log[2]]/Log[2], 10, 111][[1]] (* Robert G. Wilson v, Mar 23 2005 *) RealDigits[x/.FindRoot[x 2^x==1, {x, .6}, WorkingPrecision->100]][[1]] (* Harvey P. Dale, Apr 17 2019 *) PROG (PARI) lambertw(log(2))/log(2) \\ Stanislav Sykora, Nov 03 2013 CROSSREFS Equals 1/A030798. Cf. A073084. Sequence in context: A060780 A199391 A106333 * A117335 A319555 A244980 Adjacent sequences:  A104745 A104746 A104747 * A104749 A104750 A104751 KEYWORD nonn,cons AUTHOR Zak Seidov, Mar 23 2005 EXTENSIONS More terms from Robert G. Wilson v, Mar 23 2005 Offset corrected by R. J. Mathar, Feb 05 2009 STATUS approved

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Last modified June 13 04:04 EDT 2021. Contains 344980 sequences. (Running on oeis4.)