A194756 Number of k such that {-k*Pi} < {-n*Pi}, where { } = fractional part.

1, 1, 1, 1, 1, 1, 1, 8, 7, 6, 5, 4, 3, 2, 15, 13, 11, 9, 7, 5, 3, 22, 19, 16, 13, 10, 7, 4, 29, 25, 21, 17, 13, 9, 5, 36, 31, 26, 21, 16, 11, 6, 43, 37, 31, 25, 19, 13, 7, 50, 43, 36, 29, 22, 15, 8, 57, 49, 41, 33, 25, 17, 9, 64, 55, 46, 37, 28, 19, 10, 71, 61, 51, 41, 31

Offset

1,8

Links

Table of n, a(n) for n=1..75.

Mathematica

r = -Pi; 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}]   (* A194756 *)
Table[t[n], {n, 1, 100}]   (* A194757 *)

Crossrefs

Cf. A194757, A194738.

Sequence in context: A055119 A265338 A090915 * A132672 A212410 A328759

Adjacent sequences: A194753 A194754 A194755 * A194757 A194758 A194759

Keyword

nonn

Author

Clark Kimberling, Sep 02 2011

Status

approved