A194743 - OEIS

%I #6 Mar 30 2012 18:57:44

%S 0,0,0,0,4,3,2,1,8,6,4,2,12,9,6,3,16,12,8,4,0,17,12,7,2,22,16,10,4,27,

%T 20,13,6,32,24,16,8,0,30,21,12,3,36,26,16,6,42,31,20,9,48,36,24,12,0,

%U 43,30,17,4,50,36,22,8,57,42,27,12,64,48,32,16,0,56,39,22,5,64

%N Number of k such that {k*sqrt(5)} > {n*sqrt(5)}, where { } = fractional part.

%t r = Sqrt[5]; 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}]   (* A194742 *)

%t Table[t[n], {n, 1, 100}]   (* A194743 *)

%Y Cf. A194743, A194738.

%K nonn

%O 1,5

%A _Clark Kimberling_, Sep 02 2011