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Least m such that if r and s in {1/2, 1/5, 1/8,..., 1/(3n-1)}, satisfy r < s, then r < k/m < s for some integer k.
2

%I #11 Mar 06 2014 22:31:01

%S 3,6,17,25,45,57,86,103,141,185,209,262,321,386,421,495,575,661,706,

%T 801,902,1009,1122,1181,1303,1431,1565,1705,1777,1926,2081,2242,2409,

%U 2495,2671,2853,3041,3235,3435,3537,3746,3961,4182,4409,4642,4881,5003,5251,5505

%N Least m such that if r and s in {1/2, 1/5, 1/8,..., 1/(3n-1)}, 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="/A024823/b024823.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/(3 h - 1), {h, 1, 60}]];

%t leastSeparator[t]

%Y Cf. A001000.

%K nonn

%O 2,1

%A _Clark Kimberling_