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A024848 a(n) = least m such that if r and s in {1/2, 1/4, 1/6, ..., 1/2n} satisfy r < s, then r < k/m < (k+4)/m < s for some integer k.

%I A024848 #10 Mar 06 2014 22:37:00
%S A024848 19,53,103,169,251,349,463,593,739,901,1101,1299,1537,1769,2045,2311,
%T A024848 2625,2925,3277,3611,4001,4369,4797,5199,5665,6101,6605,7075,7617,
%U A024848 8121,8701,9301,9859,10497,11155,11765,12461,13177,13839,14593,15367,16081,16893,17725
%N A024848 a(n) = least m such that if r and s in {1/2, 1/4, 1/6, ..., 1/2n} satisfy r < s, then r < k/m < (k+4)/m < s for some integer k.
%C A024848 For a guide to related sequences, see A001000. - _Clark Kimberling_, Aug 12 2012
%H A024848 Clark Kimberling, <a href="/A024848/b024848.txt">Table of n, a(n) for n = 2..100</a>
%t A024848 leastSeparatorS[seq_, s_] := Module[{n = 1},
%t A024848 Table[While[Or @@ (Ceiling[n #1[[1]]] <
%t A024848 s + 1 + Floor[n #1[[2]]] &) /@ (Sort[#1, Greater] &) /@
%t A024848 Partition[Take[seq, k], 2, 1], n++]; n, {k, 2, Length[seq]}]];
%t A024848 t = Map[leastSeparatorS[1/(2*Range[50]), #] &, Range[5]];
%t A024848 TableForm[t]
%t A024848 t[[5]]  (* A024848 *)
%t A024848 (* _Peter J. C. Moses_, Aug 06 2012 *)
%Y A024848 Cf. A001000, A024847.
%K A024848 nonn
%O A024848 2,1
%A A024848 _Clark Kimberling_