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A024838 Least m such that if r and s in {1/3, 1/6, 1/9, ..., 1/3n} satisfy r < s, then r < k/m < (k+1)/m < s for some integer k.

%I A024838 #12 Jun 27 2022 18:53:35
%S A024838 10,25,46,73,121,166,235,295,385,460,571,661,793,937,1054,1219,1396,
%T A024838 1537,1735,1945,2110,2341,2584,2773,3037,3313,3601,3826,4135,4456,
%U A024838 4789,5047,5401,5767,6145,6436,6835,7246,7669,7993,8437,8893,9361,9841,10210,10711,11224
%N A024838 Least m such that if r and s in {1/3, 1/6, 1/9, ..., 1/3n} satisfy r < s, then r < k/m < (k+1)/m < s for some integer k.
%C A024838 For a guide to related sequences, see A001000. - _Clark Kimberling_, Aug 12 2012
%H A024838 Clark Kimberling, <a href="/A024838/b024838.txt">Table of n, a(n) for n = 2..100</a>
%t A024838 leastSeparatorS[seq_, s_] := Module[{n = 1},
%t A024838 Table[While[Or @@ (Ceiling[n #1[[1]]] <
%t A024838 s + 1 + Floor[n #1[[2]]] &) /@ (Sort[#1, Greater] &) /@
%t A024838 Partition[Take[seq, k], 2, 1], n++]; n, {k, 2, Length[seq]}]];
%t A024838 t = Map[leastSeparatorS[1/(3*Range[50]), #] &, Range[5]];
%t A024838 t[[2]] (* A024838 *)
%t A024838 (* _Peter J. C. Moses_, Aug 06 2012 *)
%Y A024838 Cf. A001000, A024836, A024837.
%K A024838 nonn
%O A024838 2,1
%A A024838 _Clark Kimberling_