A024825 a(n) = least m such that if r and s in {1/4, 1/8, 1/12,..., 1/4n} satisfy r < s, then r < k/m < s for some integer k.

5, 9, 25, 37, 65, 81, 121, 169, 197, 257, 325, 361, 441, 529, 625, 677, 785, 901, 1025, 1089, 1225, 1369, 1521, 1681, 1765, 1937, 2117, 2305, 2501, 2601, 2809, 3025, 3249, 3481, 3721, 3845, 4097, 4357, 4625, 4901, 5185, 5329, 5625, 5929, 6241

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..300

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/(4 h), {h, 1, 60}]];
leastSeparator[t]
(* Peter J. C. Moses, Aug 01 2012 *)

Extensions

Corrected and edited by Clark Kimberling, Aug 07 2012