Let $g(x)$ be a polynomial with integral coefficients.

For $r\geq 1$, We define the sequence $a_{g}$ for some polynomial $g(x)$ as follows:

$\clubsuit)a_{g}(1)=g(x)$

$\clubsuit)a_{g}(r)=g(a_{g}(r-1))$ for $r\geq 2$

Now we are given a polynomial $f(x)$ of $\deg(f)\geq 2$ such that if $x=0$, $a_{f}(r)\rightarrow\infty$ as $r$ grows large.

Then is it true that if $x=0$ then sum of reciprocal of primes $p$ such that $p|a_{f}(p)$ converges?

**P.S.An analogous result has been proven for elliptic curves by Serre.**