%I #12 Jun 27 2022 21:17:58

%S 13,33,61,97,161,221,313,393,513,613,761,881,1057,1249,1405,1625,1861,

%T 2049,2313,2593,2813,3121,3445,3697,4049,4417,4801,5101,5513,5941,

%U 6385,6729,7201,7689,8193,8581,9113,9661,10225,10657,11249,11857

%N 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 For a guide to related sequences, see A001000. - _Clark Kimberling_, Aug 12 2012

%H Clark Kimberling, <a href="/A024839/b024839.txt">Table of n, a(n) for n = 2..100</a>

%t leastSeparatorS[seq_, s_] := Module[{n = 1},

%t Table[While[Or @@ (Ceiling[n #1[[1]]] <

%t s + 1 + Floor[n #1[[2]]] &) /@ (Sort[#1, Greater] &) /@

%t Partition[Take[seq, k], 2, 1], n++]; n, {k, 2, Length[seq]}]];

%t t = Map[leastSeparatorS[1/(4*Range[50]), #] &, Range[5]];

%t t[[2]] (* A024839 *)

%t (* _Peter J. C. Moses_, Aug 06 2012 *)

%Y Cf. A001000, A024838.

%K nonn

%O 2,1

%A _Clark Kimberling_

%E Corrected by _Clark Kimberling_, Aug 12 2012