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A024839 Least m such that if r and s in {1/4, 1/8, 1/12, ..., 1/4n} satisfy r < s, then r < k/m < (k+1)/m < s for some integer k.

%I A024839 #12 Jun 27 2022 21:17:58
%S A024839 13,33,61,97,161,221,313,393,513,613,761,881,1057,1249,1405,1625,1861,
%T A024839 2049,2313,2593,2813,3121,3445,3697,4049,4417,4801,5101,5513,5941,
%U A024839 6385,6729,7201,7689,8193,8581,9113,9661,10225,10657,11249,11857
%N A024839 Least m such that if r and s in {1/4, 1/8, 1/12, ..., 1/4n} satisfy r < s, then r < k/m < (k+1)/m < s for some integer k.
%C A024839 For a guide to related sequences, see A001000. - _Clark Kimberling_, Aug 12 2012
%H A024839 Clark Kimberling, <a href="/A024839/b024839.txt">Table of n, a(n) for n = 2..100</a>
%t A024839 leastSeparatorS[seq_, s_] := Module[{n = 1},
%t A024839 Table[While[Or @@ (Ceiling[n #1[[1]]] <
%t A024839 s + 1 + Floor[n #1[[2]]] &) /@ (Sort[#1, Greater] &) /@
%t A024839 Partition[Take[seq, k], 2, 1], n++]; n, {k, 2, Length[seq]}]];
%t A024839 t = Map[leastSeparatorS[1/(4*Range[50]), #] &, Range[5]];
%t A024839 t[[2]] (* A024839 *)
%t A024839 (* _Peter J. C. Moses_, Aug 06 2012 *)
%Y A024839 Cf. A001000, A024838.
%K A024839 nonn
%O A024839 2,1
%A A024839 _Clark Kimberling_
%E A024839 Corrected by _Clark Kimberling_, Aug 12 2012