A214964 - OEIS

%I #11 Mar 01 2014 09:45:48

%S 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,

%T 34,34,34,34,34,34,34,34,43,45,50,50,50,50,55,55,55,55,55,55,55,55,55,

%U 55,55,55,55,55,55,72,73,73,73,81,81,81,81,81,81,89,89,89,89

%N 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.

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

%H Clark Kimberling, <a href="/A214964/b214964.txt">Table of n, a(n) for n = 2..300</a>

%t leastSeparatorShort[seq_, s_] := Module[{n = 1},

%t While[Or @@ (n #1[[1]] <= s + Floor[n #1[[2]]] &) /@ (Sort[#1, Greater] &) /@

%t Partition[seq, 2, 1], n++]; n];

%t Table[leastSeparatorShort[Sort[N[FractionalPart[GoldenRatio*Range[n]], 50]], 1], {n, 2, 100}]

%t (* _Peter J. C. Moses_, Aug 01 2012 *)

%Y Cf. A001000, A214961, A214965.

%K nonn

%O 2,1

%A _Clark Kimberling_, Aug 12 2012