cp's OEIS Frontend

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.

%I A214964 #11 Mar 01 2014 09:45:48
%S A214964 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 A214964 34,34,34,34,34,34,34,34,43,45,50,50,50,50,55,55,55,55,55,55,55,55,55,
%U A214964 55,55,55,55,55,55,72,73,73,73,81,81,81,81,81,81,89,89,89,89
%N 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.
%C A214964 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 A214964 Clark Kimberling, <a href="/A214964/b214964.txt">Table of n, a(n) for n = 2..300</a>
%t A214964 leastSeparatorShort[seq_, s_] := Module[{n = 1},
%t A214964 While[Or @@ (n #1[[1]] <= s + Floor[n #1[[2]]] &) /@ (Sort[#1, Greater] &) /@
%t A214964 Partition[seq, 2, 1], n++]; n];
%t A214964 Table[leastSeparatorShort[Sort[N[FractionalPart[GoldenRatio*Range[n]], 50]], 1], {n, 2, 100}]
%t A214964 (* _Peter J. C. Moses_, Aug 01 2012 *)
%Y A214964 Cf. A001000, A214961, A214965.
%K A214964 nonn
%O A214964 2,1
%A A214964 _Clark Kimberling_, Aug 12 2012