A245218 - OEIS

%I #5 Jul 17 2014 22:12:23

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

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

%U 7,1,0,7,9,0,7,6,9,8,6,2,6,0,4,6,1,6

%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 A001951, else f(n,x) = 1/x.

%C See Comments at A245215.

%H Clark Kimberling, <a href="/A245218/b245218.txt">Table of n, a(n) for n = 1..1000</a>

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

%e c = 3.43648484309813517846105390392471356500...  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}; max(S(12)) = 24/7 = 3.42857...

%t 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 m = Max[N[Table[s[n], {n, 1, 4000}], 300]]

%t t = RealDigits[m]  (* A245217 *)

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

%Y Cf. A226080 (infinite Fibonacci tree), A245215, A245217, A245219, A245223.

%K nonn,cons,easy

%O 1,1

%A _Clark Kimberling_, Jul 13 2014