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A245219 Continued fraction expansion of the constant c in A245218; c = 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. 5
3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See Comments at A245215.

Likely a duplicate of A097509. - R. J. Mathar, Jul 21 2014

LINKS

Table of n, a(n) for n=1..86.

EXAMPLE

c = 3.43648484... ; 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, with continued fraction [3,2,3].

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]]]; max = Max[N[Table[s[n], {n, 1, 3000}], 200]] (* A245217 *)

ContinuedFraction[max, 120] (* A245219 *)

CROSSREFS

Cf. A226080 (infinite Fibonacci tree), A245217, A245218, A245222, A245225.

Sequence in context: A082844 A279124 A101406 * A097509 A095206 A308006

Adjacent sequences:  A245216 A245217 A245218 * A245220 A245221 A245222

KEYWORD

nonn,cofr,easy

AUTHOR

Clark Kimberling, Jul 13 2014

STATUS

approved

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Last modified June 16 12:38 EDT 2019. Contains 324152 sequences. (Running on oeis4.)