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A194756 Number of k such that {-k*Pi} < {-n*Pi}, where { } = fractional part.

%I A194756 #8 Apr 10 2021 08:04:51
%S A194756 1,1,1,1,1,1,1,8,7,6,5,4,3,2,15,13,11,9,7,5,3,22,19,16,13,10,7,4,29,
%T A194756 25,21,17,13,9,5,36,31,26,21,16,11,6,43,37,31,25,19,13,7,50,43,36,29,
%U A194756 22,15,8,57,49,41,33,25,17,9,64,55,46,37,28,19,10,71,61,51,41,31
%N A194756 Number of k such that {-k*Pi} < {-n*Pi}, where { } = fractional part.
%t A194756 r = -Pi; p[x_] := FractionalPart[x];
%t A194756 u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0]
%t A194756 v[n_, k_] := If[p[k*r] > p[n*r], 1, 0]
%t A194756 s[n_] := Sum[u[n, k], {k, 1, n}]
%t A194756 t[n_] := Sum[v[n, k], {k, 1, n}]
%t A194756 Table[s[n], {n, 1, 100}]   (* A194756 *)
%t A194756 Table[t[n], {n, 1, 100}]   (* A194757 *)
%Y A194756 Cf. A194757, A194738.
%K A194756 nonn
%O A194756 1,8
%A A194756 _Clark Kimberling_, Sep 02 2011