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.

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

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

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

Adjacent sequences: A024837 A024838 A024839 * A024841 A024842 A024843

Keyword

nonn

Author

Clark Kimberling

Status

approved