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%I #18 Jul 25 2019 01:00:53
%S 4,11,29,173,1063,7074,47753,325961,2228269,15262701,104577551,
%T 716721983,4912208209
%N a(n) = least m such that if r and s in {F(2*h-1)/F(2*h): h = 1,2,...,n} satisfy r < s, then r < k/m < s for some integer k, where F = A000045 (Fibonacci numbers).
%C For a guide to related sequences, see A001000. - _Clark Kimberling_, Aug 07 2012
%t leastSeparator[seq_] := Module[{n = 1},
%t Table[While[Or @@ (Ceiling[n #1[[1]]] <
%t 2 + Floor[n #1[[2]]] &) /@ (Sort[#1, Greater] &) /@
%t Partition[Take[seq, k], 2, 1], n++]; n, {k, 2, Length[seq]}]];
%t t = Table[N[Fibonacci[2 h - 1]/Fibonacci[2 h]], {h, 1, 10}]
%t t1 = leastSeparator[t]
%t (* _Peter J. C. Moses_, Aug 01 2012 *)
%Y Cf. A001000, A024830.
%K nonn,more
%O 2,1
%A _Clark Kimberling_
%E Corrected by _Clark Kimberling_, Aug 07 2012
%E a(11)-a(14) from _Sean A. Irvine_, Jul 25 2019