A024821 - OEIS

%I #13 Mar 01 2014 09:57:52

%S 4,5,9,11,17,21,25,32,40,43,55,61,67,73,87,94,105,113,125,137,145,153,

%T 166,179,188,202,216,226,246,256,271,281,297,307,329,340,351,368,385,

%U 403,421,439,451,469,481,500,519,538,551,564,584,604,624,645,666,687,708,722,743

%N Least m such that if r and s in {1/sqrt(h): h = 1,2,...,n} satisfy r < s, then r < k/m < s for some integer k.

%C For a guide to related sequences, see A001000. - _Clark Kimberling_, Aug 07 2012

%H Clark Kimberling, <a href="/A024821/b024821.txt">Table of n, a(n) for n = 2..200</a>

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

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

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

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

%t t = Flatten[Table[1/Sqrt[h], {h, 1, 60}]];

%t leastSeparator[t]

%t (* _Peter J. C. Moses_, Aug 01 2012 *)

%Y Cf. A001000.

%K nonn

%O 2,1

%A _Clark Kimberling_