A194737 Number of k such that {-k*sqrt(2)} > {-n*sqrt(2)}, where { } = fractional part.

0, 1, 0, 2, 0, 3, 6, 2, 6, 1, 6, 11, 4, 10, 2, 9, 0, 8, 16, 5, 14, 2, 12, 22, 8, 19, 4, 16, 0, 13, 26, 8, 22, 3, 18, 33, 12, 28, 6, 23, 40, 16, 34, 9, 28, 2, 22, 42, 14, 35, 6, 28, 50, 19, 42, 10, 34, 1, 26, 51, 16, 42, 6, 33, 60, 22, 50, 11, 40, 69, 28, 58, 16, 47, 4, 36

Offset

1,4

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. A194736, A194738.

Sequence in context: A011120 A256930 A226210 * A071089 A144090 A330674

Adjacent sequences: A194734 A194735 A194736 * A194738 A194739 A194740

Keyword

nonn

Author

Clark Kimberling, Sep 02 2011

Status

approved