On arithmetical nature of Tichy-Uitz's function

R.F.Tichy and J.Uitz introduced a one parameter family $g_{\lambda}$, $\lambda \in (0,1)$, of singular functions. When $\lambda=1/2$ the function $g_{\lambda}$ coincides with the famous Minkowski question mark function. In this paper we describe the arithmetical nature of the function $g_{\lambda}$ when $\lambda = \frac{3-\sqrt{5}}{2}$.