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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. 4
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, 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, 7, 1, 0, 7, 9, 0, 7, 6, 9, 8, 6, 2, 6, 0, 4, 6, 1, 6 (list; constant; graph; refs; listen; history; text; internal format)
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 = 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...

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

t = RealDigits[m]  (* A245217 *)

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

CROSSREFS

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

Sequence in context: A021295 A061112 A078809 * A097857 A176058 A110738

Adjacent sequences:  A245215 A245216 A245217 * A245219 A245220 A245221

KEYWORD

nonn,cons,easy

AUTHOR

Clark Kimberling, Jul 13 2014

STATUS

approved

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Last modified September 27 13:48 EDT 2021. Contains 347688 sequences. (Running on oeis4.)