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URL: https://oeis.org/A024846

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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.
3
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
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
KEYWORD
nonn
STATUS
approved