%I #25 Aug 09 2023 16:59:28
%S 2,8,2,1,4,3,9,3,7,2,1,2,2,0,7,8,8,9,3,4,0,3,1,9,1,3,3,0,2,9,4,4,8,5,
%T 1,9,5,3,4,5,8,8,1,7,4,4,0,7,3,1,1,4,0,9,2,2,7,9,8,5,7,6,9,3,9,4,1,2,
%U 1,4,3,0,4,5,0,5,5,1,7,3,9,1,2,4,5,6,8,6,5,6,5,3,4,7,8,3,9,6,4,4,3,8,9,5,9
%N Decimal expansion of the positive solution to x = 3*(1-exp(-x)).
%C The positive solution to x=3*(1-exp(-x)) is the dimensionless coefficient corresponding to the maximum brightness in Planck's law of radiation.
%C It can be symbolically expressed as 3+W(-3/e^3), where W stands for Lambert (a.k.a. "ProductLog") function.
%H Stanislav Sykora, <a href="/A194567/b194567.txt">Table of n, a(n) for n = 1..2000</a>
%H SpectralCalc, <a href="http://www.spectralcalc.com/blackbody/blackbody.html">Calculation of Blackbody Radiance</a>, Appendix C.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Planck%27s_law">Planck's law</a>
%e 2.821439372...
%t RealDigits[ N[x /. ToRules[ Reduce[x > 0 && x == 3*(1 - E^-x), x, Reals]], 100]][[1]]
%t RealDigits[3 + ProductLog[-3/E^3], 10, 111][[1]] (* _Robert G. Wilson v_, Oct 16 2013 *)
%t RealDigits[x/.FindRoot[x==3(1-Exp[-x]),{x,2},WorkingPrecision->120]][[1]] (* _Harvey P. Dale_, Aug 09 2023 *)
%o (PARI) a3=solve(x=0.1,10,x-3*(1-exp(-x))) \\ Use real precision in excess
%o (PARI) 3+lambertw(-3/exp(3)) \\ _Charles R Greathouse IV_, Sep 13 2022
%Y Cf. A094090, A256500, A256501.
%K nonn,cons
%O 1,1
%A _Jean-François Alcover_, Aug 29 2011
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