A024825 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,1

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

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]}]];