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A024849 a(n) = least m such that if r and s in {|F(h+1)-tau*F(h)|: h = 1,2,...,n} satisfy r < s, then r < k/m < s for some integer k, where F = A000045 (Fibonacci numbers) and tau = (1+sqrt(5))/2 (golden ratio). 1
2, 4, 6, 9, 14, 23, 36, 59, 94, 153, 246, 399, 644, 1043, 1686, 2729, 4414, 7143, 11556, 18699 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

For a guide to related sequences, see A001000. - Clark Kimberling, Aug 12 2012

LINKS

Table of n, a(n) for n=2..21.

MATHEMATICA

f[n_] := Fibonacci[n]; r = GoldenRatio;

leastSeparator[seq_] := Module[{n = 1},

Table[While[Or @@ (Ceiling[n #1[[1]]] <

2 + Floor[n #1[[2]]] &) /@ (Sort[#1, Greater] &) /@

Partition[Take[seq, k], 2, 1], n++]; n, {k, 2, Length[seq]}]];

t = Flatten[Table[Abs[f[h + 1] - r*f[h]], {h, 1, 21}]];

leastSeparator[t]

(* Peter J. C. Moses, Aug 01 2012 *)

CROSSREFS

Cf. A000045, A001000, A001622.

Sequence in context: A005687 A164139 A218605 * A323227 A283024 A090483

Adjacent sequences:  A024846 A024847 A024848 * A024850 A024851 A024852

KEYWORD

nonn,more

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified January 26 13:09 EST 2022. Contains 350598 sequences. (Running on oeis4.)