  Let $$\gamma^*:=\frac{8}{9}+\frac{2}{3}\:\frac{\log(10/9)}{\log 10}\:(\approx
0.919\ldots)\:,\ \gamma^*<\frac{1}{c_0}\leq 1\:.$$
  Let $\gamma^*<\gamma_0\leq 1$, $c_0=1/\gamma_0$ be fixed. Let also
$a_0\in\{0,1,\ldots, 9\}$. In [23] we proved on assumption of the Generalized
Riemann Hypothesis (GRH), that each sufficiently large odd integer $N_0$ can be
represented in the form $$N_0=p_1+p_2+p_3\:,$$ where for $i=2, 3$ the primes
$p_i$ are Piatetski-Shapiro primes - primes of the form $p_i=[n_i^{c_0}]$,
$n_i\in\mathbb{N}$ - whereas the decimal expansion of $p_1$ does not contain
the digit $a_0$. In this paper we replace one of the Piatetski-Shapiro primes
$p_2$ and $p_3$ by primes of the type $$p=x^2+y^2+1\:.$$
