A194736 Number of k such that {-k*sqrt(2)} < {-n*sqrt(2)}, where { } = fractional part.

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

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}]   (* A194736 *)
Table[t[n], {n, 1, 100}]   (* A194737 *)

Crossrefs

Cf. A194737, A194738.

Sequence in context: A106615 A361317 A361783 * A333363 A130299 A143309

Adjacent sequences: A194733 A194734 A194735 * A194737 A194738 A194739

Keyword

nonn

Author

Clark Kimberling, Sep 02 2011

Status

approved