A024835 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+1)/m < s for some integer k.

7, 17, 31, 49, 81, 111, 157, 197, 257, 307, 381, 441, 529, 625, 703, 813, 931, 1025, 1157, 1297, 1407, 1561, 1723, 1849, 2025, 2209, 2401, 2551, 2757, 2971, 3193, 3365, 3601, 3845, 4097, 4291, 4557, 4831, 5113, 5329, 5625, 5929, 6241, 6561, 6807, 7141, 7483, 7833

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[[2]] (* A024835 *)
(* Peter J. C. Moses, Aug 06 2012 *)

Crossrefs

Cf. A001000, A024834.

Sequence in context: A130284 A056220 A024840 * A225251 A178491 A319304

Adjacent sequences: A024832 A024833 A024834 * A024836 A024837 A024838

Keyword

nonn

Author

Clark Kimberling

Status

approved