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A194755 Number of integers k in 1..n such that {k*Pi} > {n*Pi}, where { } = fractional part.

%I A194755 #14 Apr 10 2021 23:56:52
%S A194755 0,0,0,0,0,0,0,7,6,5,4,3,2,1,14,12,10,8,6,4,2,21,18,15,12,9,6,3,28,24,
%T A194755 20,16,12,8,4,35,30,25,20,15,10,5,42,36,30,24,18,12,6,49,42,35,28,21,
%U A194755 14,7,56,48,40,32,24,16,8,63,54,45,36,27,18,9,70,60,50,40,30,20
%N A194755 Number of integers k in 1..n such that {k*Pi} > {n*Pi}, where { } = fractional part.
%t A194755 r = Pi; p[x_] := FractionalPart[x];
%t A194755 u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0]
%t A194755 v[n_, k_] := If[p[k*r] > p[n*r], 1, 0]
%t A194755 s[n_] := Sum[u[n, k], {k, 1, n}]
%t A194755 t[n_] := Sum[v[n, k], {k, 1, n}]
%t A194755 Table[s[n], {n, 1, 100}]   (* A194754 *)
%t A194755 Table[t[n], {n, 1, 100}]   (* A194755 *)
%Y A194755 Cf. A194754, A194738.
%K A194755 nonn
%O A194755 1,8
%A A194755 _Clark Kimberling_, Sep 02 2011
%E A194755 Name clarified by _Jon E. Schoenfield_, Apr 10 2021