Valeurs polynomiales sous contraintes digitales

For an integer $q \geq 2$ and $n \in \mathbb{N}$, we denote by $s_q(n)$ the sum of the digits of the integer $n$ written in base $q$. We are interested in the study of almost prime values $(F(n))_{n \in \mathbb{N}}$ of a given polynomial $F \in \mathbb{Z}[X]$, under the condition $s_q(n) \equiv a \pmod{b}$, where $b, q \geq 2$ are integers such that $\gcd(b, q - 1) = 1$.