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A194746 Number of k such that {k*sqrt(6)} < {n*sqrt(6)}, where { } = fractional part.

%I A194746 #5 Mar 30 2012 18:57:44
%S A194746 1,2,1,3,1,4,1,5,1,6,11,5,11,4,11,3,11,2,11,20,9,19,7,18,5,17,3,16,1,
%T A194746 15,29,12,27,9,25,6,23,3,21,39,17,36,13,33,9,30,5,27,1,24,47,19,43,14,
%U A194746 39,9,35,4,31,58,25,53,19,48,13,43,7,38,1,33,65,26,59,19,53,12
%N A194746 Number of k such that {k*sqrt(6)} < {n*sqrt(6)}, where { } = fractional part.
%t A194746 r = Sqrt[6]; p[x_] := FractionalPart[x];
%t A194746 u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0]
%t A194746 v[n_, k_] := If[p[k*r] > p[n*r], 1, 0]
%t A194746 s[n_] := Sum[u[n, k], {k, 1, n}]
%t A194746 t[n_] := Sum[v[n, k], {k, 1, n}]
%t A194746 Table[s[n], {n, 1, 100}]   (* A194746 *)
%t A194746 Table[t[n], {n, 1, 100}]   (* A194747 *)
%Y A194746 Cf. A194747, A194738.
%K A194746 nonn
%O A194746 1,2
%A A194746 _Clark Kimberling_, Sep 02 2011