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A024828 a(n) = least m such that if r and s in {h/(1 + h^2): h = 1,2,...,n} satisfy r < s, then r < k/m < s for some integer k.

%I A024828 #12 Mar 01 2014 09:56:58
%S A024828 7,9,11,14,18,27,32,44,58,66,83,102,112,134,158,184,198,227,258,291,
%T A024828 308,344,382,422,464,486,531,578,627,678,704,758,814,872,932,994,1026,
%U A024828 1091,1158,1227,1298,1371,1408,1484,1562,1642,1724,1808,1894,1938,2027,2118,2211,2306
%N A024828 a(n) = least m such that if r and s in {h/(1 + h^2): h = 1,2,...,n} satisfy r < s, then r < k/m < s for some integer k.
%C A024828 For a guide to related sequences, see A001000. - _Clark Kimberling_, Aug 07 2012
%H A024828 Clark Kimberling, <a href="/A024828/b024828.txt">Table of n, a(n) for n = 2..200</a>
%t A024828 leastSeparator[seq_] := Module[{n = 1},
%t A024828 Table[While[Or @@ (Ceiling[n #1[[1]]] <
%t A024828 2 + Floor[n #1[[2]]] &) /@ (Sort[#1, Greater] &) /@
%t A024828 Partition[Take[seq, k], 2, 1], n++]; n, {k, 2, Length[seq]}]];
%t A024828 t = Flatten[Table[h/(1 + h^2), {h, 1, 60}]]
%t A024828 leastSeparator[t]
%t A024828 (* _Peter J. C. Moses_, Aug 01 2012 *)
%Y A024828 Cf. A001000.
%K A024828 nonn
%O A024828 2,1
%A A024828 _Clark Kimberling_