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A194757 Number of k such that {-k*Pi} > {-n*Pi}, where { } = fractional part.

%I A194757 #8 Apr 10 2021 08:04:58
%S A194757 0,1,2,3,4,5,6,0,2,4,6,8,10,12,0,3,6,9,12,15,18,0,4,8,12,16,20,24,0,5,
%T A194757 10,15,20,25,30,0,6,12,18,24,30,36,0,7,14,21,28,35,42,0,8,16,24,32,40,
%U A194757 48,0,9,18,27,36,45,54,0,10,20,30,40,50,60,0,11,22,33,44,55,66
%N A194757 Number of k such that {-k*Pi} > {-n*Pi}, where { } = fractional part.
%t A194757 r = -Pi; p[x_] := FractionalPart[x];
%t A194757 u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0]
%t A194757 v[n_, k_] := If[p[k*r] > p[n*r], 1, 0]
%t A194757 s[n_] := Sum[u[n, k], {k, 1, n}]
%t A194757 t[n_] := Sum[v[n, k], {k, 1, n}]
%t A194757 Table[s[n], {n, 1, 100}]   (* A194756 *)
%t A194757 Table[t[n], {n, 1, 100}]   (* A194757 *)
%Y A194757 Cf. A194756, A194738.
%K A194757 nonn
%O A194757 1,3
%A A194757 _Clark Kimberling_, Sep 02 2011