A024846 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+4)/m < s for some integer k.

11, 29, 55, 89, 131, 181, 239, 305, 379, 461, 551, 661, 769, 898, 1023, 1171, 1313, 1480, 1639, 1825, 2001, 2206, 2399, 2623, 2833, 3076, 3303, 3565, 3809, 4090, 4351, 4651, 4961, 5249, 5578, 5917, 6231, 6589, 6957, 7297, 7684, 8081, 8447, 8863, 9289, 9681, 10126

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 5th separator of the set {1/3, 1/2, 1} is a(3) = 29, since 1/3 < 10/29 < 14/29 < 1/2 < 15/29 < 19/29 < 1, and 29 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[[5]] (* Peter J. C. Moses, Aug 08 2012 *)

Crossrefs

Cf. A001000.

Sequence in context: A039316 A364894 A082108 * A024842 A304275 A031072

Adjacent sequences: A024843 A024844 A024845 * A024847 A024848 A024849

Keyword

nonn

Author

Clark Kimberling

Status

approved