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A194742 Number of k such that {k*sqrt(5)} < {n*sqrt(5)}, where { } = fractional part.

%I A194742 #5 Mar 30 2012 18:57:44
%S A194742 1,2,3,4,1,3,5,7,1,4,7,10,1,5,9,13,1,6,11,16,21,5,11,17,23,4,11,18,25,
%T A194742 3,11,19,27,2,11,20,29,38,9,19,29,39,7,18,29,40,5,17,29,41,3,16,29,42,
%U A194742 55,13,27,41,55,10,25,40,55,7,23,39,55,4,21,38,55,72,17,35,53
%N A194742 Number of k such that {k*sqrt(5)} < {n*sqrt(5)}, where { } = fractional part.
%t A194742 r = Sqrt[5]; p[x_] := FractionalPart[x];
%t A194742 u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0]
%t A194742 v[n_, k_] := If[p[k*r] > p[n*r], 1, 0]
%t A194742 s[n_] := Sum[u[n, k], {k, 1, n}]
%t A194742 t[n_] := Sum[v[n, k], {k, 1, n}]
%t A194742 Table[s[n], {n, 1, 100}]   (* A194742 *)
%t A194742 Table[t[n], {n, 1, 100}]   (* A194743 *)
%Y A194742 Cf. A194743, A194738.
%K A194742 nonn
%O A194742 1,2
%A A194742 _Clark Kimberling_, Sep 02 2011