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A024826 Least m such that if r and s in {1/1, 1/3, 1/6,..., 1/C(n+1,2)} satisfy r < s, then r < k/m < s for some integer k.

%I A024826 #11 Mar 06 2014 22:31:11
%S A024826 2,4,7,13,31,46,64,85,145,181,226,331,397,469,638,736,841,1089,1225,
%T A024826 1378,1711,1901,2311,2542,2784,3313,3601,3901,4564,4915,5685,6091,
%U A024826 6526,7441,7937,8977,9538,10116,11341,11989,13358,14080,14821,16401,17221,18964,19867
%N A024826 Least m such that if r and s in {1/1, 1/3, 1/6,..., 1/C(n+1,2)} satisfy r < s, then r < k/m < s for some integer k.
%C A024826 For a guide to related sequences, see A001000. - _Clark Kimberling_, Aug 07 2012
%H A024826 Clark Kimberling, <a href="/A024826/b024826.txt">Table of n, a(n) for n = 2..100</a>
%t A024826 leastSeparator[seq_] := Module[{n = 1},
%t A024826 Table[While[Or @@ (Ceiling[n #1[[1]]] <
%t A024826 2 + Floor[n #1[[2]]] &) /@ (Sort[#1, Greater] &) /@
%t A024826 Partition[Take[seq, k], 2, 1], n++]; n, {k, 2, Length[seq]}]];
%t A024826 t = Flatten[Table[1/Binomial[h + 1, 2], {h, 1, 50}]]
%t A024826 leastSeparator[t]
%Y A024826 Cf. A001000.
%K A024826 nonn
%O A024826 2,1
%A A024826 _Clark Kimberling_