A194736 - OEIS

%I #8 Jun 06 2018 16:17:42

%S 1,1,3,2,5,3,1,6,3,9,5,1,9,4,13,7,17,10,3,15,7,20,11,2,17,7,23,12,29,

%T 17,5,24,11,31,17,3,25,10,33,17,1,26,9,35,17,44,25,6,35,15,45,24,3,35,

%U 13,46,23,57,33,9,45,20,57,31,5,44,17,57,29,1,43,14,57,27,71,40

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

%H G. C. Greubel, <a href="/A194736/b194736.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}]   (* A194736 *)

%t Table[t[n], {n, 1, 100}]   (* A194737 *)

%Y Cf. A194737, A194738.

%K nonn

%O 1,3

%A _Clark Kimberling_, Sep 02 2011