A245224 - OEIS

%I #4 Jul 20 2014 00:14:43

%S 2,7,0,7,7,7,8,7,1,6,0,0,5,0,7,8,1,2,4,3,4,0,2,0,6,6,6,5,9,6,3,1,3,1,

%T 6,2,9,9,2,3,3,1,2,4,2,4,9,1,0,4,4,5,1,7,6,6,6,9,1,3,7,9,1,8,3,4,6,4,

%U 8,3,0,8,8,4,3,2,3,4,7,0,0,2,3,5,5,3

%N Decimal expansion of sup{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 See Comments at A245215.

%H Clark Kimberling, <a href="/A245224/b245224.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n)*inf{f(n,1)} = 1.

%e c = 2.7077787160050781243402066659631316299233...  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 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 m = Max[N[Table[s[n], {n, 1, 4000}], 300]]

%t RealDigits[m]  (* A245224 *)

%t (* _Peter J. C. Moses_, Jul 04 2014 *)

%Y Cf. A226080 (infinite Fibonacci tree), A245215, A245217, A245220, A245224.

%K nonn,cons,easy

%O 1,1

%A _Clark Kimberling_, Jul 14 2014