A024573 a(n) = floor(1/frac(n*e)).

1, 2, 6, 1, 1, 3, 35, 1, 2, 5, 1, 1, 2, 17, 1, 2, 4, 1, 1, 2, 11, 1, 1, 4, 1, 1, 2, 8, 1, 1, 3, 1, 1, 2, 7, 1, 1, 3, 76, 1, 2, 5, 1, 1, 3, 24, 1, 2, 5, 1, 1, 2, 14, 1, 1, 4, 1, 1, 2, 10, 1, 1, 3, 1, 1, 2, 8, 1, 1, 3, 1, 1, 2, 6, 1, 1, 3, 38, 1, 2, 5, 1, 1, 2, 18, 1, 2, 4, 1, 1, 2, 12, 1, 1, 4, 1, 1, 2, 9, 1

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Comments

From Hieronymus Fischer, Apr 15 2012: (Start)

The sequence is well defined, since frac(n*e)>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*e) is uniformly distributed. (End)

Links

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

Crossrefs

Cf. A024584, A022843, A000142, A000027.

Cf. A190860, A190847.

Programs

Maple

seq(floor(1/frac(n*exp(1))), n=1..30); # Ridouane Oudra, Jun 09 2025

Mathematica

f[n_] := Floor[1/FractionalPart[n*E]]; Array[f, 100] (* Robert G. Wilson v, Apr 17 2012 *)

Formula

From Ridouane Oudra, Jun 09 2025: (Start)

a(n!) = n.

a(n) = 1 if n is in A190860.

a(n) > 1 if n is in A190847. (End)