A024827 - OEIS

A024827

Least m such that if r and s in {1/1, 1/4, 1/9,..., 1/n^2} satisfy r < s, then r < k/m < s for some integer k.

%I #11 Mar 06 2014 22:31:20

%S 2,5,10,19,33,76,109,148,197,325,406,501,727,865,1015,1373,1576,1801,

%T 2313,2602,3250,3611,4001,4852,5325,5820,6913,7501,8789,9478,10207,

%U 11775,12616,14416,15377,16385,18514,19653,22051,23329,24643,27437,28900,32001,33621

%N Least m such that if r and s in {1/1, 1/4, 1/9,..., 1/n^2} 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="/A024827/b024827.txt">Table of n, a(n) for n = 2..100</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

%t [seq]}]];

%t t = Flatten[Table[1/h^2, {h, 1, 60}]]

%t leastSeparator[t]

%Y Cf. A001000.

%K nonn

%O 2,1

%A _Clark Kimberling_