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A194747 Number of k such that {k*sqrt(6)} > {n*sqrt(6)}, where { } = fractional part. 3

%I

%S 0,0,2,1,4,2,6,3,8,4,0,7,2,10,4,13,6,16,8,0,12,3,16,6,20,9,24,12,28,

%T 15,2,20,6,25,10,30,14,35,18,1,24,6,30,11,36,16,42,21,48,26,4,33,10,

%U 40,16,47,22,54,28,2,36,9,44,16,52,23,60,30,68,37,6,46,14,55,22,64

%N Number of k such that {k*sqrt(6)} > {n*sqrt(6)}, where { } = fractional part.

%t r = Sqrt[6]; 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}] (* A194746 *)

%t Table[t[n], {n, 1, 100}] (* A194747 *)

%Y Cf. A194746, A194738.

%K nonn

%O 1,3

%A _Clark Kimberling_, Sep 02 2011

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Last modified July 28 12:14 EDT 2021. Contains 346328 sequences. (Running on oeis4.)