A024834 a(n) = least m such that if r and s in {1/1, 1/3, 1/5, ..., 1/(2n-1)} satisfy r < s, then r < k/m < (k+1)/m < s for some integer k.

4, 13, 26, 43, 64, 100, 133, 183, 226, 290, 343, 421, 484, 576, 676, 757, 871, 993, 1090, 1226, 1370, 1483, 1641, 1807, 1936, 2116, 2304, 2500, 2653, 2863, 3081, 3307, 3482, 3722, 3970, 4226, 4423, 4693, 4971, 5257, 5476, 5776, 6084, 6400, 6724, 6973, 7311, 7657, 8011

Offset

2,1

Comments

For a guide to related sequences, see A001000. - Clark Kimberling, Aug 12 2012

Links

Clark Kimberling, Table of n, a(n) for n = 2..100

Mathematica

leastSeparatorS[seq_, s_] := Module[{n = 1},
Table[While[Or @@ (Ceiling[n #1[[1]]] <
s + 1 + Floor[n #1[[2]]] &) /@ (Sort[#1, Greater] &) /@
Partition[Take[seq, k], 2, 1], n++]; n, {k, 2, Length[seq]}]];
t = Map[leastSeparatorS[1/(2*Range[50] - 1), #] &, Range[5]];
t[[2]] (* A024834 *)
(* Peter J. C. Moses, Aug 06 2012 *)

Crossrefs

Cf. A001000, A024835.

Sequence in context: A333297 A092484 A091823 * A143867 A024809 A212901

Adjacent sequences: A024831 A024832 A024833 * A024835 A024836 A024837

Keyword

nonn

Author

Clark Kimberling

Status

approved