A024828 a(n) = least m such that if r and s in {h/(1 + h^2): h = 1,2,...,n} satisfy r < s, then r < k/m < s for some integer k.

7, 9, 11, 14, 18, 27, 32, 44, 58, 66, 83, 102, 112, 134, 158, 184, 198, 227, 258, 291, 308, 344, 382, 422, 464, 486, 531, 578, 627, 678, 704, 758, 814, 872, 932, 994, 1026, 1091, 1158, 1227, 1298, 1371, 1408, 1484, 1562, 1642, 1724, 1808, 1894, 1938, 2027, 2118, 2211, 2306

Offset: 2

Author

Clark Kimberling

Keywords

• nonn

Comments

For a guide to related sequences, see A001000. - Clark Kimberling, Aug 07 2012

Links

• Clark Kimberling, Table of n, a(n) for n = 2..200

Crossrefs

Cf. A001000.

Programs

Mathematica

leastSeparator[seq_] := Module[{n = 1},
Table[While[Or @@ (Ceiling[n #1[[1]]] <
2 + Floor[n #1[[2]]] &) /@ (Sort[#1, Greater] &) /@
Partition[Take[seq, k], 2, 1], n++]; n, {k, 2, Length[seq]}]];
t = Flatten[Table[h/(1 + h^2), {h, 1, 60}]]
leastSeparator[t]
(* Peter J. C. Moses, Aug 01 2012 *)