A194735 Number of positive integers k <= n such that {k*sqrt(2)} > {n*sqrt(2)}, where { } = fractional part.

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

Offset

1,3

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Mathematica

r = Sqrt[2]; p[x_] := FractionalPart[x];
u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0]
v[n_, k_] := If[p[k*r] > p[n*r], 1, 0]
s[n_] := Sum[u[n, k], {k, 1, n}]
t[n_] := Sum[v[n, k], {k, 1, n}]
Table[s[n], {n, 1, 100}]   (* A054072 *)
Table[t[n], {n, 1, 100}]   (* A194735 *)

Crossrefs

Cf. A054072, A194738.

Sequence in context: A016445 A244554 A364953 * A130544 A214027 A007739

Adjacent sequences: A194732 A194733 A194734 * A194736 A194737 A194738

Keyword

nonn

Author

Clark Kimberling, Sep 02 2011

Status

approved