A214964 Least m > 0 such that for every r and s in the set S = {{h*(1+sqrt(5))/2} : h = 1,..,n} of fractional parts, if r < s, then r < k/m < s for some integer k; m is the least separator of S as defined at A001000.

2, 3, 4, 5, 6, 8, 8, 10, 10, 13, 13, 13, 16, 16, 16, 21, 21, 21, 21, 21, 28, 30, 30, 30, 34, 34, 34, 34, 34, 34, 34, 34, 34, 43, 45, 50, 50, 50, 50, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 72, 73, 73, 73, 81, 81, 81, 81, 81, 81, 89, 89, 89, 89

Offset

2,1

Comments

a(n) is the least separator of S, as defined at A001000, which includes a guide to related sequences. - Clark Kimberling, Aug 12 2012

Links

Clark Kimberling, Table of n, a(n) for n = 2..300

Mathematica

leastSeparatorShort[seq_, s_] := Module[{n = 1},
While[Or @@ (n #1[[1]] <= s + Floor[n #1[[2]]] &) /@ (Sort[#1, Greater] &) /@
Partition[seq, 2, 1], n++]; n];
Table[leastSeparatorShort[Sort[N[FractionalPart[GoldenRatio*Range[n]], 50]], 1], {n, 2, 100}]
(* Peter J. C. Moses, Aug 01 2012 *)

Crossrefs

Cf. A001000, A214961, A214965.

Sequence in context: A130916 A003965 A351988 * A097502 A318122 A265568

Adjacent sequences: A214961 A214962 A214963 * A214965 A214966 A214967

Keyword

nonn

Author

Clark Kimberling, Aug 12 2012

Status

approved