A024839 Least m such that if r and s in {1/4, 1/8, 1/12, ..., 1/4n} satisfy r < s, then r < k/m < (k+1)/m < s for some integer k.

13, 33, 61, 97, 161, 221, 313, 393, 513, 613, 761, 881, 1057, 1249, 1405, 1625, 1861, 2049, 2313, 2593, 2813, 3121, 3445, 3697, 4049, 4417, 4801, 5101, 5513, 5941, 6385, 6729, 7201, 7689, 8193, 8581, 9113, 9661, 10225, 10657, 11249, 11857

Offset: 2

Author

Clark Kimberling

Keywords

• nonn

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

Crossrefs

Cf. A001000, A024838.

Programs

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/(4*Range[50]), #] &, Range[5]];
t[[2]] (* A024839 *)
(* Peter J. C. Moses, Aug 06 2012 *)

Extensions

Corrected by Clark Kimberling, Aug 12 2012