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A194751 Number of k such that {k*e} > {n*e}, where { } = fractional part.

%I A194751 #6 Mar 30 2012 18:57:44
%S A194751 0,1,2,0,2,4,6,1,4,7,0,4,8,12,2,7,12,0,6,12,18,3,10,17,0,8,16,24,4,13,
%T A194751 22,0,10,20,30,5,16,27,38,10,22,34,4,17,30,43,10,24,38,3,18,33,48,10,
%U A194751 26,42,2,19,36,53,10,28,46,1,20,39,58,10,30,50,0,21,42,63,10,32
%N A194751 Number of k such that {k*e} > {n*e}, where { } = fractional part.
%t A194751 r = E; p[x_] := FractionalPart[x];
%t A194751 u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0]
%t A194751 v[n_, k_] := If[p[k*r] > p[n*r], 1, 0]
%t A194751 s[n_] := Sum[u[n, k], {k, 1, n}]
%t A194751 t[n_] := Sum[v[n, k], {k, 1, n}]
%t A194751 Table[s[n], {n, 1, 100}]   (* A194750 *)
%t A194751 Table[t[n], {n, 1, 100}]   (* A194751 *)
%Y A194751 Cf. A194750, A194738.
%K A194751 nonn
%O A194751 1,3
%A A194751 _Clark Kimberling_, Sep 02 2011