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

2,1

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

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 *)

Crossrefs

Cf. A001000.

Sequence in context: A029612 A120165 A267970 * A139058 A242103 A328454

Adjacent sequences: A024825 A024826 A024827 * A024829 A024830 A024831

Keyword

nonn

Author

Clark Kimberling

Status

approved