A245224 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.

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

Offset

1,1

Comments

See Comments at A245215.

Links

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

Formula

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

Example

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...

Mathematica

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;
m = Max[N[Table[s[n], {n, 1, 4000}], 300]]
RealDigits[m]  (* A245224 *)
(* Peter J. C. Moses, Jul 04 2014 *)

Crossrefs

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

Sequence in context: A372386 A199273 A196833 * A016638 A199398 A296453

Adjacent sequences: A245221 A245222 A245223 * A245225 A245226 A245227

Keyword

nonn,cons,easy

Author

Clark Kimberling, Jul 14 2014

Status

approved