A024842 a(n) = least m such that if r and s in {1/2, 1/4, 1/6, ..., 1/2n} satisfy r < s, then r < k/m < (k+2)/m < s for some integer k.

11, 29, 55, 89, 131, 181, 253, 323, 417, 505, 621, 727, 865, 989, 1149, 1291, 1473, 1633, 1837, 2053, 2243, 2481, 2731, 2949, 3221, 3505, 3751, 4057, 4375, 4649, 4989, 5341, 5643, 6017, 6403, 6733, 7141, 7561, 7993, 8363, 8817, 9283, 9761, 10169, 10669, 11181, 11705

Offset

2,1

Comments

For a guide to related sequences, see A001000. - Clark Kimberling, Aug 12 2012

Links

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

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/(2*Range[50]), #] &, Range[5]];
t[[3]] (* A024842 *)
(* Peter J. C. Moses, Aug 06 2012 *)

Crossrefs

Cf. A001000, A024841.

Sequence in context: A364894 A082108 A024846 * A304275 A031072 A193880

Adjacent sequences: A024839 A024840 A024841 * A024843 A024844 A024845

Keyword

nonn

Author

Clark Kimberling

Status

approved