cp's OEIS Frontend

A226574 Decimal expansion of lim_{k->oo} f(k), where f(1)=e, and f(k) = e + log(f(k-1)) for k>1.

%I A226574 #12 May 29 2020 02:20:01
%S A226574 4,1,3,8,6,5,1,9,4,6,4,7,9,1,2,8,6,9,3,8,1,8,7,0,8,7,5,5,2,5,2,4,3,5,
%T A226574 4,7,8,3,4,3,6,7,4,4,3,0,4,6,4,8,5,4,8,1,1,2,9,4,4,3,1,6,3,9,3,5,4,0,
%U A226574 5,1,8,4,4,3,6,7,5,5,3,9,3,0,4,2,7,1
%N A226574 Decimal expansion of lim_{k->oo} f(k), where f(1)=e, and f(k) = e + log(f(k-1)) for k>1.
%C A226574 Let g(x) be the greater of the two solutions of s + log(s) = x; then A226572 represents g(e). [See however the comments in A226571. - _N. J. A. Sloane_, Dec 09 2017]
%H A226574 Clark Kimberling, <a href="/A226574/b226574.txt">Table of n, a(n) for n = 1..1000</a>
%F A226574 Equals -LambertW(-1, -exp(-e)). - _Jianing Song_, Dec 24 2018
%e A226574 limit(f(n)) = 4.1386519474...
%t A226574 f[s_, accuracy_] := FixedPoint[N[s - Log[#], accuracy] &, 1]
%t A226574 g[s_, accuracy_] := FixedPoint[N[s + Log[#], accuracy] &, 1]
%t A226574 d1 = RealDigits[f[E, 200]][[1]]   (* A226573 *)
%t A226574 d2 = RealDigits[g[E, 200]][[1]]  (* A226574 *)
%o A226574 (PARI) default(realprecision, 100); solve(x=4, 5, x - log(x) - exp(1)) \\ _Jianing Song_, Dec 24 2018
%Y A226574 Cf. A226571, A226572, A226573.
%K A226574 nonn,cons,easy
%O A226574 1,1
%A A226574 _Clark Kimberling_, Jun 12 2013
%E A226574 Definition revised by _N. J. A. Sloane_, Dec 09 2017