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%I #21 Nov 06 2018 11:33:30
%S 2,0,1,6,7,7,9,7,6,4,8,9,2,2,0,0,6,2,4,2,7,7,7,9,0,5,5,4,1,9,4,0,1,1,
%T 7,3,3,7,7,2,6,1,7,8,3,6,7,6,3,7,0,6,4,0,2,4,4,1,0,3,3,0,7,2,1,4,2,7,
%U 5,0,5,7,4,4,9,0,9,8,9,9,9,9,1,5,2,4
%N Decimal expansion of lim_{k->oo} f(k), where f(1)=e, and f(k) = e - log(f(k-1)) for k>1.
%C Old definition was: Decimal digits of limit(f(n)), where f(1) = e-log(e), f(n) = f(f(n-1)).
%C Let f(x) be lesser of the two solutions of s - log(s) = x; then A226571 represents f(e). [See however the comments in A226571. - _N. J. A. Sloane_, Dec 09 2017]
%H Clark Kimberling, <a href="/A226573/b226573.txt">Table of n, a(n) for n = 1..10000</a>
%F Equals LambertW(e^e). - _Clark Kimberling_, Feb 15 2018
%e limit(f(n)) = 2.0167797639...
%t Program 1:
%t f[s_, accuracy_] := FixedPoint[N[s - Log[#], accuracy] &, 1]
%t g[s_, accuracy_] := FixedPoint[N[s + Log[#], accuracy] &, 1]
%t d1 = RealDigits[f[E, 200]][[1]] (* A226573 *)
%t d2 = RealDigits[g[E, 200]][[1]] (* A226574 *)
%t s /. NSolve[s - Log[s] == 2, 200] (* both constants *)
%t ***
%t Program 2:
%t N[ProductLog[E^E], 100] (* _Clark Kimberling_, Feb 15 2018 *)
%o (PARI) default(realprecision, 100); lambertw(exp(exp(1))) \\ _G. C. Greubel_, Sep 09 2018
%Y Cf. A226571, A226572, A226574.
%K nonn,cons,easy
%O 1,1
%A _Clark Kimberling_, Jun 12 2013
%E Definition revised by _N. J. A. Sloane_, Dec 09 2017
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