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A024820 a(n) = least m such that if r and s in {1/2, 1/4, 1/6,..., 1/2n} satisfy r < s, then r < k/m < s for some integer k.

%I A024820 #13 Mar 06 2014 22:30:34
%S A024820 3,5,13,19,33,41,61,85,99,129,163,181,221,265,313,339,393,451,513,545,
%T A024820 613,685,761,841,883,969,1059,1153,1251,1301,1405,1513,1625,1741,1861,
%U A024820 1923,2049,2179,2313,2451,2593,2665,2813,2965,3121,3281,3445,3613,3699,3873,4051,4233
%N A024820 a(n) = least m such that if r and s in {1/2, 1/4, 1/6,..., 1/2n} satisfy r < s, then r < k/m < s for some integer k.
%C A024820 For a guide to related sequences, see A001000. - _Clark Kimberling_, Aug 07 2012
%H A024820 Clark Kimberling, <a href="/A024820/b024820.txt">Table of n, a(n) for n = 2..300</a>
%t A024820 leastSeparator[t_] := Module[{n = 1},
%t A024820 Table[While[Or @@ (Ceiling[n #1[[1]]] <
%t A024820 2 + Floor[n #1[[2]]] &) /@ (Sort[#1, Greater] &) /@
%t A024820 Partition[Take[t, k], 2, 1], n++]; n, {k, 2, Length[t]}]];
%t A024820 t = Flatten[{1/(2*Range[60])}]
%t A024820 leastSeparator[t]
%Y A024820 Cf. A001000.
%K A024820 nonn
%O A024820 2,1
%A A024820 _Clark Kimberling_