A024584 a(n) = floor(1/frac(n*Pi)).

7, 3, 2, 1, 1, 1, 1, 7, 3, 2, 1, 1, 1, 1, 8, 3, 2, 1, 1, 1, 1, 8, 3, 2, 1, 1, 1, 1, 9, 4, 2, 1, 1, 1, 1, 10, 4, 2, 1, 1, 1, 1, 11, 4, 2, 1, 1, 1, 1, 12, 4, 2, 1, 1, 1, 1, 14, 4, 2, 2, 1, 1, 1, 16, 4, 2, 2, 1, 1, 1, 18, 5, 2, 2, 1, 1, 1, 22, 5, 3, 2, 1, 1, 1, 28, 5, 3, 2, 1, 1, 1, 37, 5, 3, 2, 1, 1, 1, 56, 6

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Comments

From Hieronymus Fischer, Apr 15 2012: (Start)

The sequence is well defined, since frac(n*Pi)>0 for n>0.

Let b(n,m)=|{a(k)| 1<=k<=n, a(k)>=m}| be the number of the first n terms which are >= m >= 1.

Then, lim b(n,m)/n = 1/m for n-->oo since frac(n*pi) is uniformly distributed. (End)

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A024753, A022844.

Programs

Mathematica

Table[Floor[1/FractionalPart[n Pi]], {n, 100}] (* Bruno Berselli, Apr 15 2012 *)

PARI

a(n) = floor(1/frac(n*Pi)); \\ Michel Marcus, Nov 16 2022