  Recently, motivated by Stanley sequences, Kiss, S\' andor and Yang introduced
a new type sequence: a sequence $A$ of nonnegative integers is called an $AP_k$
- covering sequence if there exists an integer $n_0$ such that if $n > n_0$,
then there exist $a_1\in A, \dots , a_{k-1}\in A$, $a_1<a_2<\cdots <a_{k-1}<n$
such that $a_1, \dots , a_{k-1}, n$ form a $k$-term arithmetic progression.
They prove that there exists an $AP_3$ - covering sequence $A$ such that
$\limsup\limits_{n\to\infty}{A(n)}/{\sqrt n}\le 34$. In this note, we prove
that there exists an $AP_3$ - covering sequence $A$ such that
$\limsup\limits_{n\to\infty}{A(n)}/{\sqrt n}=\sqrt{15}$.
