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A024824 a(n) = least m such that if r and s in {1/3, 1/6, 1/9,..., 1/3n} satisfy r < s, then r < k/m < s for some integer k.

%I A024824 #13 Mar 01 2014 09:57:31
%S A024824 4,7,19,28,49,61,91,127,148,193,244,271,331,397,469,508,589,676,769,
%T A024824 817,919,1027,1141,1261,1324,1453,1588,1729,1876,1951,2107,2269,2437,
%U A024824 2611,2791,2884,3073,3268,3469,3676,3889,3997,4219,4447,4681,4921,5167,5419,5548
%N A024824 a(n) = least m such that if r and s in {1/3, 1/6, 1/9,..., 1/3n} satisfy r < s, then r < k/m < s for some integer k.
%C A024824 For a guide to related sequences, see A001000. - _Clark Kimberling_, Aug 07 2012
%H A024824 Clark Kimberling, <a href="/A024824/b024824.txt">Table of n, a(n) for n = 2..300</a>
%t A024824 leastSeparator[seq_] := Module[{n = 1},
%t A024824 Table[While[Or @@ (Ceiling[n #1[[1]]] <
%t A024824 2 + Floor[n #1[[2]]] &) /@ (Sort[#1, Greater] &) /@
%t A024824 Partition[Take[seq, k], 2, 1], n++]; n, {k, 2, Length[seq]}]];
%t A024824 t = Flatten[Table[1/(3 n), {n, 1, 60}]];
%t A024824 leastSeparator[t]
%t A024824 (* _Peter J. C. Moses_, Aug 01 2012 *)
%Y A024824 Cf. A001000.
%K A024824 nonn
%O A024824 2,1
%A A024824 _Clark Kimberling_