cp's OEIS Frontend

A245218 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.

%I A245218 #5 Jul 17 2014 22:12:23
%S A245218 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 A245218 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 A245218 7,1,0,7,9,0,7,6,9,8,6,2,6,0,4,6,1,6
%N A245218 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 A245218 See Comments at A245215.
%H A245218 Clark Kimberling, <a href="/A245218/b245218.txt">Table of n, a(n) for n = 1..1000</a>
%F A245218 a(n)*inf{f(n,1)} = 1.
%e A245218 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 A245218 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 A245218 m = Max[N[Table[s[n], {n, 1, 4000}], 300]]
%t A245218 t = RealDigits[m]  (* A245217 *)
%t A245218 (* _Peter J. C. Moses_, Jul 04 2014 *)
%Y A245218 Cf. A226080 (infinite Fibonacci tree), A245215, A245217, A245219, A245223.
%K A245218 nonn,cons,easy
%O A245218 1,1
%A A245218 _Clark Kimberling_, Jul 13 2014