proposed

approved

editing

proposed

allocated for Clark KimberlingDecimal 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.

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

1,1

See Comments at A245215.

Clark Kimberling, <a href="/A245220/b245220.txt">Table of n, a(n) for n = 1..1000</a>

a(n)*sup{f(n,1)} = 1.

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...

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;

m = Min[N[Table[s[n], {n, 1, 4000}], 300]]

t = RealDigits[m] (* A245220 *)

(* Peter J. C. Moses, Jul 04 2014 *)

Cf. A226080 (infinite Fibonacci tree), A245215, A245217, A245221, A245222.

allocated

nonn,cons,easy

Clark Kimberling, Jul 14 2014

approved

editing

allocated for Clark Kimberling

allocated

approved