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A194740 Number of k such that {-k*sqrt(3)} < {-n*sqrt(3)}, where { } = fractional part.

%I A194740 #5 Mar 30 2012 18:57:44
%S A194740 1,2,3,1,3,5,7,2,5,8,11,3,7,11,1,6,11,16,3,9,15,21,5,12,19,26,7,15,23,
%T A194740 2,11,20,29,5,15,25,35,8,19,30,41,11,23,35,3,16,29,42,7,21,35,49,11,
%U A194740 26,41,1,17,33,49,6,23,40,57,11,29,47,65,16,35,54,3,23,43,63,9
%N A194740 Number of k such that {-k*sqrt(3)} < {-n*sqrt(3)}, where { } = fractional part.
%t A194740 Remove["Global`*"];
%t A194740 r = -Sqrt[3]; p[x_] := FractionalPart[x];
%t A194740 u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0]
%t A194740 v[n_, k_] := If[p[k*r] > p[n*r], 1, 0]
%t A194740 s[n_] := Sum[u[n, k], {k, 1, n}]
%t A194740 t[n_] := Sum[v[n, k], {k, 1, n}]
%t A194740 Table[s[n], {n, 1, 100}]   (* A194740 *)
%t A194740 Table[t[n], {n, 1, 100}]   (* A194741 *)
%Y A194740 Cf. A194741, A194738.
%K A194740 nonn
%O A194740 1,2
%A A194740 _Clark Kimberling_, Sep 02 2011