smc

We construct the following table: $$\begin{array}{cccccccccccc}& & & & & & & & & & & \\ [-2.5ex]\text{Term}& {\mathbf{D}}_0& {\mathbf{D}}_1& {\mathbf{D}}_2& {\mathbf{D}}_3& {\mathbf{D}}_4& {\mathbf{D}}_5& {\mathbf{D}}_6& {\mathbf{D}}_7& {\mathbf{D}}_8& {\mathbf{D}}_9& \cdots \\ & & & & & & & & & & & \\ [-2.25ex]\text{Value}& 0& 0& 1& 1& 1& 2& 3& 4& 6& 9& \cdots \\ & & & & & & & & & & & \\ [-2.25ex]\text{Parity}& E& E& O& O& O& E& O& E& E& O& \cdots \end{array}$$ Note that $(D_7,D_8,D_9)$ and $(D_0,D_1,D_2)$ have the same parities, so the parity is periodic with period $7.$ Since the remainders of $(2021÷7,2022÷7,2023÷7)$ are $(5,6,7),$ we conclude that $(D_{2021},D_{2022},D_{2023})$ and $(D_5,D_6,D_7)$ have the same parities, namely $\boxed{(E,O,E)}.$