A024843 a(n) = least m such that if r and s in {1/1, 1/2, 1/3, ..., 1/n} satisfy r < s, then r < k/m < (k+3)/m < s for some integer k.

9, 23, 43, 69, 101, 139, 183, 233, 289, 361, 431, 518, 601, 703, 799, 916, 1025, 1157, 1279, 1426, 1561, 1723, 1871, 2048, 2209, 2401, 2601, 2783, 2998, 3221, 3423, 3661, 3907, 4129, 4390, 4659, 4901, 5185, 5477, 5739, 6046, 6361, 6643, 6973, 7311, 7613, 7966, 8327, 8649

Offset

2,1

Comments

For a guide to related sequences, see A001000. - Clark Kimberling, Aug 08 2012

Links

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

Example

Using the terminology introduced at A001000, the 4th separator of the set {1/3, 1/2, 1} is a(3) = 23, since 1/3 < 8/23 < 11/23 < 1/2 < 12/23 < 15/23 < 1 and 23 is the least m for which 1/3, 1/2, 1 are thus separated using numbers k/m. - Clark Kimberling, Aug 08 2012

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/Range[50], #] &, Range[5]];
TableForm[t]
t[[4]] (* Peter J. C. Moses, Aug 08 2012 *)

Crossrefs

Cf. A001000.

Sequence in context: A147395 A302906 A144390 * A363161 A183453 A296311

Adjacent sequences: A024840 A024841 A024842 * A024844 A024845 A024846

Keyword

nonn

Author

Clark Kimberling

Status

approved