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.

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

Offset: 1

Author

Clark Kimberling, Jul 13 2014

Keywords

• nonn
• cons
• easy

Comments

See Comments at A245215.

Examples

			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...
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A226080 (infinite Fibonacci tree), A245215, A245218, A245220, A245223.

Programs

Mathematica

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;
m = Min[N[Table[s[n], {n, 1, 4000}], 300]]
t = RealDigits[m]  (* A245217 *)
(* Peter J. C. Moses, Jul 04 2014 *)

Formula

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