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A024840
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+2)/m < s for some integer k.
2
7, 17, 31, 49, 71, 97, 127, 169, 209, 262, 311, 375, 433, 508, 575, 661, 737, 834, 919, 1027, 1141, 1241, 1366, 1497, 1611, 1753, 1901, 2029, 2188, 2353, 2495, 2671, 2853, 3009, 3202, 3401, 3571, 3781, 3997, 4219, 4409, 4642, 4881, 5126, 5335, 5591, 5853, 6121, 6349, 6628
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 3rd separator of the set {1/3, 1/2, 1} is a(3) = 17, since 1/3 < 6/17 < 8/17 < 1/2 < 8/17 < 10/17 < 1 and 17 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[[3]] (* Peter J. C. Moses, Aug 08 2012 *)
CROSSREFS
Cf. A001000.
Sequence in context: A120092 A130284 A056220 * A024835 A225251 A178491
KEYWORD
nonn
STATUS
approved