  Tang and Ding \cite{X. Tang} present a series of quaternary sequences $w(a,
b)$ interleaved by two binary sequences $a$ and $b$ with ideal autocorrelation
and show that such interleaved quaternary sequences have optimal
autocorrelation. In this paper we consider the 4-adic complexity $FC_{w}(4)$ of
such quaternary sequence $w=w(a, b)$. We present a general formula on
$FC_{w}(4)$, $w=w(a, b)$. As a direct consequence, we obtain a general lower
bound $FC_{w}(4)\geq\log_{4}(4^{n}-1)$ where $2n$ is the period of the sequence
$w$. By taking $a$ and $b$ to be several types of known binary sequences with
ideal autocorrelation ($m$-sequences, twin-prime, Legendre, Hall sequences and
their complement, shift or sample sequences), we compute the exact values of
$FC_{w}(4)$, $w=w(a, b)$ and show that in most cases $FC_{w}(4)$ reaches or
nearly reaches the maximum value $\log_{4}(4^{2n}-1)$. Our results show that
the 4-adic complexity of the quaternary sequences defined in \cite{X. Tang} are
large enough to resist the attack of the rational approximation algorithm.
