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A245223 Decimal expansion of inf{f(n,1)}, where f(1,x) = x + 1 and thereafter f(n,x) = x + 1 if n is in A054385, else f(n,x) = 1/x.

%I A245223 #4 Jul 20 2014 00:14:34
%S A245223 3,6,9,3,0,6,3,9,6,4,5,3,0,1,2,3,0,5,9,7,2,7,8,1,6,9,3,6,8,7,1,9,0,6,
%T A245223 6,9,4,4,5,6,3,1,3,3,1,6,9,0,3,8,4,9,6,0,5,3,1,0,9,1,0,0,2,8,8,6,3,3,
%U A245223 4,6,9,2,4,5,3,0,2,7,0,1,2,6,2,9,8,0
%N A245223 Decimal expansion of inf{f(n,1)}, where f(1,x) = x + 1 and thereafter f(n,x) = x + 1 if n is in A054385, else f(n,x) = 1/x.
%C A245223 See Comments at A245215.
%H A245223 Clark Kimberling, <a href="/A245223/b245223.txt">Table of n, a(n) for n = 1..1000</a>
%F A245223 a(n)*sup{f(n,1)} = 1.
%e A245223 c = 0.36930639645301230597278169368719066944...  The first 16 numbers f(n,1) comprise S(16) = {1, 2, 1/2, 3/2, 5/2, 2/5, 7/5, 12/5, 5/12, 17/12, 12/17, 29/17}; min(S(16)) = 17/46 = 0.36956... and max(S(12)) = 46/17 = 2.7058...
%t A245223 tmpRec = $RecursionLimit; $RecursionLimit = Infinity; u[x_] := u[x] = x + 1; d[x_] := d[x] = 1/x; r = E/(E-1); w = Table[Floor[k*r], {k, 2000}]; s[1] = 1; s[n_] := s[n] = If[MemberQ[w, n - 1], u[s[n - 1]], d[s[n - 1]]]; $RecursionLimit = tmpRec;
%t A245223 m = Min[N[Table[s[n], {n, 1, 4000}], 300]]
%t A245223 RealDigits[m]  (* A245223 *)
%t A245223 (* _Peter J. C. Moses_, Jul 04 2014 *)
%Y A245223 Cf. A226080 (infinite Fibonacci tree), A245215, A245217, A245220, A245224.
%K A245223 nonn,cons,easy
%O A245223 1,1
%A A245223 _Clark Kimberling_, Jul 14 2014