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A245220 Decimal expansion of inf{f(n,1)}, where f(1,x) = x + 1 and thereafter f(n,x) = x + 1 if n is in A022838, else f(n,x) = 1/x.

%I A245220 #4 Jul 17 2014 22:13:30
%S A245220 3,6,7,5,4,3,4,9,1,1,8,4,9,5,1,2,4,8,7,2,1,2,6,0,9,7,2,5,4,1,0,9,2,5,
%T A245220 4,0,7,0,8,3,4,4,0,8,8,6,0,5,2,0,6,3,6,5,9,3,6,0,9,1,7,8,7,0,4,6,9,2,
%U A245220 5,9,5,1,9,7,4,4,3,5,6,0,6,2,5,8,0,2
%N A245220 Decimal expansion of inf{f(n,1)}, where f(1,x) = x + 1 and thereafter f(n,x) = x + 1 if n is in A022838, else f(n,x) = 1/x.
%C A245220 See Comments at A245215.
%H A245220 Clark Kimberling, <a href="/A245220/b245220.txt">Table of n, a(n) for n = 1..1000</a>
%F A245220 a(n)*sup{f(n,1)} = 1.
%e A245220 c = 0.367543491184951248721260972541092540...  The first 12 numbers f(n,1) comprise S(12) = {1, 2, 1/2, 3/2, 2/3, 5/3, 8/3, 3/8, 11/8, 8/11, 19/11, 11/19}; min(S(12)) = 3/8 = 0.375... and max(S(12)) = 8/3 = 2.666...
%t A245220 tmpRec = $RecursionLimit; $RecursionLimit = Infinity; u[x_] := u[x] = x + 1; d[x_] := d[x] = 1/x; r = Sqrt[3]; 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 A245220 m = Min[N[Table[s[n], {n, 1, 4000}], 300]]
%t A245220 t = RealDigits[m]  (* A245220 *)
%t A245220 (* _Peter J. C. Moses_, Jul 04 2014 *)
%Y A245220 Cf. A226080 (infinite Fibonacci tree), A245215, A245217, A245221, A245222.
%K A245220 nonn,cons,easy
%O A245220 1,1
%A A245220 _Clark Kimberling_, Jul 14 2014