A194735 - OEIS

%I #14 Jan 28 2018 11:05:58

%S 0,0,2,1,4,2,0,5,2,8,4,0,8,3,12,6,16,9,2,14,6,19,10,1,16,6,22,11,28,

%T 16,4,23,10,30,16,2,24,9,32,16,0,25,8,34,16,43,24,5,34,14,44,23,2,34,

%U 12,45,22,56,32,8,44,19,56,30,4,43,16,56,28,0,42,13,56,26,70,39

%N Number of positive integers k <= n such that {k*sqrt(2)} > {n*sqrt(2)}, where { } = fractional part.

%H G. C. Greubel, <a href="/A194735/b194735.txt">Table of n, a(n) for n = 1..5000</a>

%t r = Sqrt[2]; 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}]   (* A054072 *)

%t Table[t[n], {n, 1, 100}]   (* A194735 *)

%Y Cf. A054072, A194738.

%K nonn

%O 1,3

%A _Clark Kimberling_, Sep 02 2011