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URL: https://oeis.org/A024833

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A024833
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+1)/m < s for some integer k.
2
5, 11, 19, 29, 41, 61, 79, 106, 129, 163, 191, 232, 265, 313, 365, 407, 466, 529, 579, 649, 723, 781, 862, 947, 1013, 1105, 1201, 1301, 1379, 1486, 1597, 1712, 1801, 1923, 2049, 2179, 2279, 2416, 2557, 2702, 2813, 2965, 3121, 3281, 3445, 3571, 3742, 3917, 4096
OFFSET
2,1
COMMENTS
For a guide to related sequences, see A001000. - Peter J. C. Moses, Aug 08 2012
LINKS
EXAMPLE
Using the terminology introduced at A001000, the 2nd separator of the set {1/3, 1/2, 1} is a(3) = 11, since 1/3 < 4/11 < 5/11 < 1/2 < 6/11 < 7/11 < 1 and 11 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[[2]] (* Clark Kimberling, Aug 08 2012 *)
CROSSREFS
KEYWORD
nonn
STATUS
approved