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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

For a guide to related sequences, see A001000. - Peter J. C. Moses, Aug 08 2012

LINKS

Clark Kimberling, Table of n, a(n) for n = 2..300

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

Cf. A001000, A071111, A024843, A024846.

Sequence in context: A028387 A106071 A073847 * A002327 A078179 A045451

Adjacent sequences: A024830 A024831 A024832 * A024834 A024835 A024836

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified December 5 07:25 EST 2022. Contains 358582 sequences. (Running on oeis4.)