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A024849
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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).
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1
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2, 4, 6, 9, 14, 23, 36, 59, 94, 153, 246, 399, 644, 1043, 1686, 2729, 4414, 7143, 11556, 18699
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OFFSET
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2,1
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COMMENTS
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LINKS
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MATHEMATICA
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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]
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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