  Let $S=\langle a_1,\ldots,a_p\rangle$ be a numerical semigroup, $s\in S$ and
${\sf z}(s)$ its set of factorizations. The set of length is denoted by
${\mathcal L}(s)=\{{\tt L}(x_1,\dots,x_p)\mid (x_1,\dots,x_p)\in{\sf Z}(s)\}$
where ${\tt L}(x_1,\dots,x_p)=x_1+\ldots+x_p$. From these definitions, the
following sets can be defined ${\textsf W}(n)=\{s\in S\mid \exists x\in{\sf
z}(s) \textrm{ such that } {\tt{L}}(x)=n\}$, $\nu(n)=\cup_{s\in {\textsf W}(n)}
{\mathcal L}(s)=\{l_1<l_2<\ldots< l_r\}$ and
$\Delta\nu(n)=\{l_2-l_1,\ldots,l_r-l_{r-1}\}$. In this paper, we prove that the
set $\Delta\nu(S)=\cup_{n\in{\mathbb{N}}}\Delta\nu(n)$ is almost periodic with
period ${\rm lcm}(a_1,a_p)$.
