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A024827 Least m such that if r and s in {1/1, 1/4, 1/9,..., 1/n^2} satisfy r < s, then r < k/m < s for some integer k.

%I A024827 #11 Mar 06 2014 22:31:20
%S A024827 2,5,10,19,33,76,109,148,197,325,406,501,727,865,1015,1373,1576,1801,
%T A024827 2313,2602,3250,3611,4001,4852,5325,5820,6913,7501,8789,9478,10207,
%U A024827 11775,12616,14416,15377,16385,18514,19653,22051,23329,24643,27437,28900,32001,33621
%N A024827 Least m such that if r and s in {1/1, 1/4, 1/9,..., 1/n^2} satisfy r < s, then r < k/m < s for some integer k.
%C A024827 For a guide to related sequences, see A001000. - _Clark Kimberling_, Aug 07 2012
%H A024827 Clark Kimberling, <a href="/A024827/b024827.txt">Table of n, a(n) for n = 2..100</a>
%t A024827 leastSeparator[seq_] := Module[{n = 1},
%t A024827 Table[While[Or @@ (Ceiling[n #1[[1]]] <
%t A024827 2 + Floor[n #1[[2]]] &) /@ (Sort[#1, Greater] &) /@
%t A024827 Partition[Take[seq, k], 2, 1], n++]; n, {k, 2, Length
%t A024827 [seq]}]];
%t A024827 t = Flatten[Table[1/h^2, {h, 1, 60}]]
%t A024827 leastSeparator[t]
%Y A024827 Cf. A001000.
%K A024827 nonn
%O A024827 2,1
%A A024827 _Clark Kimberling_