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A194754 Number of integers k in 1..n such that {k*Pi} < {n*Pi}, where { } = fractional part.

%I A194754 #13 Apr 10 2021 23:59:19
%S A194754 1,2,3,4,5,6,7,1,3,5,7,9,11,13,1,4,7,10,13,16,19,1,5,9,13,17,21,25,1,
%T A194754 6,11,16,21,26,31,1,7,13,19,25,31,37,1,8,15,22,29,36,43,1,9,17,25,33,
%U A194754 41,49,1,10,19,28,37,46,55,1,11,21,31,41,51,61,1,12,23,34,45,56
%N A194754 Number of integers k in 1..n such that {k*Pi} < {n*Pi}, where { } = fractional part.
%t A194754 r = Pi; p[x_] := FractionalPart[x];
%t A194754 u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0]
%t A194754 v[n_, k_] := If[p[k*r] > p[n*r], 1, 0]
%t A194754 s[n_] := Sum[u[n, k], {k, 1, n}]
%t A194754 t[n_] := Sum[v[n, k], {k, 1, n}]
%t A194754 Table[s[n], {n, 1, 100}]   (* A194754 *)
%t A194754 Table[t[n], {n, 1, 100}]   (* A194755 *)
%Y A194754 Cf. A194755, A194738.
%K A194754 nonn
%O A194754 1,2
%A A194754 _Clark Kimberling_, Sep 02 2011
%E A194754 Name clarified by _Jon E. Schoenfield_, Apr 10 2021