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A245217 Decimal expansion of inf{f(n,1)}, where f(1,x) = x + 1 and thereafter f(n,x) = x + 1 if n is in A001951, else f(n,x) = 1/x.

%I A245217 #5 Jul 17 2014 22:12:15
%S A245217 2,9,0,9,9,5,0,2,7,0,8,6,5,9,0,6,3,0,7,4,0,5,1,1,6,6,8,1,8,3,7,7,7,6,
%T A245217 5,1,3,8,5,4,3,2,0,1,6,1,0,9,6,3,8,8,9,9,6,6,2,3,6,0,5,9,9,9,3,0,5,6,
%U A245217 4,4,0,8,2,9,8,2,1,1,8,9,6,3,0,3,3,1
%N A245217 Decimal expansion of inf{f(n,1)}, where f(1,x) = x + 1 and thereafter f(n,x) = x + 1 if n is in A001951, else f(n,x) = 1/x.
%C A245217 See Comments at A245215.
%H A245217 Clark Kimberling, <a href="/A245217/b245217.txt">Table of n, a(n) for n = 1..1000</a>
%F A245217 a(n)*sup{f(n,1)} = 1.
%e A245217 c = 0.29099502708659063074051166818377765138543201...  The first 12 numbers f(n,1) comprise S(12) = {1, 2, 3, 1/3, 4/3, 7/3, 3/7, 10/7, 17/7, 24/7, 7/24, 31/24}; min(S(12)) = 7/24 = 0.29166...
%t A245217 tmpRec = $RecursionLimit; $RecursionLimit = Infinity; u[x_] := u[x] = x + 1; d[x_] := d[x] = 1/x; r = Sqrt[2]; 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 A245217 m = Min[N[Table[s[n], {n, 1, 4000}], 300]]
%t A245217 t = RealDigits[m]  (* A245217 *)
%t A245217 (* _Peter J. C. Moses_, Jul 04 2014 *)
%Y A245217 Cf. A226080 (infinite Fibonacci tree), A245215, A245218, A245220, A245223.
%K A245217 nonn,cons,easy
%O A245217 1,1
%A A245217 _Clark Kimberling_, Jul 13 2014