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A194750 Number of k such that {k*e} < {n*e}, where { } = fractional part.

%I A194750 #5 Mar 30 2012 18:57:44
%S A194750 1,1,1,4,3,2,1,7,5,3,11,8,5,2,13,9,5,18,13,8,3,19,13,7,25,18,11,4,25,
%T A194750 17,9,32,23,14,5,31,21,11,1,30,19,8,39,27,15,3,37,24,11,47,33,19,5,44,
%U A194750 29,14,55,39,23,7,51,34,17,63,45,27,9,58,39,20,71,51,31,11,65
%N A194750 Number of k such that {k*e} < {n*e}, where { } = fractional part.
%t A194750 r = E; p[x_] := FractionalPart[x];
%t A194750 u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0]
%t A194750 v[n_, k_] := If[p[k*r] > p[n*r], 1, 0]
%t A194750 s[n_] := Sum[u[n, k], {k, 1, n}]
%t A194750 t[n_] := Sum[v[n, k], {k, 1, n}]
%t A194750 Table[s[n], {n, 1, 100}]   (* A194750 *)
%t A194750 Table[t[n], {n, 1, 100}]   (* A194751 *)
%Y A194750 Cf. A194751.
%K A194750 nonn
%O A194750 1,4
%A A194750 _Clark Kimberling_, Sep 02 2011