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A024821 Least m such that if r and s in {1/sqrt(h): h = 1,2,...,n} satisfy r < s, then r < k/m < s for some integer k.

%I A024821 #13 Mar 01 2014 09:57:52
%S A024821 4,5,9,11,17,21,25,32,40,43,55,61,67,73,87,94,105,113,125,137,145,153,
%T A024821 166,179,188,202,216,226,246,256,271,281,297,307,329,340,351,368,385,
%U A024821 403,421,439,451,469,481,500,519,538,551,564,584,604,624,645,666,687,708,722,743
%N A024821 Least m such that if r and s in {1/sqrt(h): h = 1,2,...,n} satisfy r < s, then r < k/m < s for some integer k.
%C A024821 For a guide to related sequences, see A001000. - _Clark Kimberling_, Aug 07 2012
%H A024821 Clark Kimberling, <a href="/A024821/b024821.txt">Table of n, a(n) for n = 2..200</a>
%t A024821 leastSeparator[seq_] := Module[{n = 1},
%t A024821 Table[While[Or @@ (Ceiling[n #1[[1]]] <
%t A024821 2 + Floor[n #1[[2]]] &) /@ (Sort[#1, Greater] &) /@
%t A024821 Partition[Take[seq, k], 2, 1], n++]; n, {k, 2, Length[seq]}]];
%t A024821 t = Flatten[Table[1/Sqrt[h], {h, 1, 60}]];
%t A024821 leastSeparator[t]
%t A024821 (* _Peter J. C. Moses_, Aug 01 2012 *)
%Y A024821 Cf. A001000.
%K A024821 nonn
%O A024821 2,1
%A A024821 _Clark Kimberling_