A194765 - OEIS

%I #5 Mar 30 2012 18:57:44

%S 0,1,2,0,2,4,6,1,4,7,10,2,6,10,14,3,8,13,18,4,10,16,22,5,12,19,0,8,16,

%T 24,2,11,20,29,4,14,24,34,6,17,28,39,8,20,32,44,10,23,36,49,12,26,40,

%U 1,16,31,46,4,20,36,52,7,24,41,58,10,28,46,64,13,32,51,70,16,36

%N Number of k such that {-k*2^(1/3)} > {-n*2^(1/3)}, where { } = fractional part.

%t r = -2^(1/3); p[x_] := FractionalPart[x];

%t u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0]

%t v[n_, k_] := If[p[k*r] > p[n*r], 1, 0]

%t s[n_] := Sum[u[n, k], {k, 1, n}]

%t t[n_] := Sum[v[n, k], {k, 1, n}]

%t Table[s[n], {n, 1, 100}]  (* A194764 *)

%t Table[t[n], {n, 1, 100}]  (* A194765 *)

%Y Cf. A194764, A194738.

%K nonn

%O 1,3

%A _Clark Kimberling_, Sep 02 2011