A024822 a(n) = least m such that if r and s in {1/1, 1/4, 1/7,..., 1/(3n-2)} satisfy r < s, then r < k/m < s for some integer k.

2, 5, 9, 22, 31, 53, 81, 97, 134, 177, 201, 253, 311, 342, 409, 482, 561, 603, 691, 785, 885, 937, 1046, 1161, 1282, 1409, 1475, 1611, 1753, 1901, 2055, 2215, 2297, 2466, 2641, 2822, 3009, 3202, 3301, 3503, 3711, 3925, 4145, 4371, 4486, 4721

Offset: 2

Author

Clark Kimberling

Keywords

• nonn

Comments

For a guide to related sequences, see A001000. - Clark Kimberling, Aug 07 2012

Links

• Clark Kimberling, Table of n, a(n) for n = 2..200

Crossrefs

Cf. A001000.

Programs

Mathematica

leastSeparator[seq_] := Module[{n = 1},
Table[While[Or @@ (Ceiling[n #1[[1]]] <
2 + Floor[n #1[[2]]] &) /@ (Sort[#1, Greater] &) /@
Partition[Take[seq, k], 2, 1], n++]; n, {k, 2, Length[seq]}]];
t = Flatten[Table[1/(3 h - 2), {h, 1, 60}]];
leastSeparator[t]

Extensions

Corrected by Clark Kimberling, Aug 07 2012