Question 25
S3 (POL). For an integer $x\ge1$, let $p(x)$ be the least prime that does not divide $x$, and define $q(x)$ to be the product of all primes less than $p(x)$. In particular, $p(1)=2$. For $x$ such that $p(x)=2$, define $q(x)=1$. Consider the sequence $x_0,x_1,x_2,\ldots$ defined by $x_0=1$ and
$$x_{n+1}=\frac{x_np(x_n)}{q(x_n)}$$
for $n\ge0$. Find all $n$ such that $x_n=1995$.
$$x_{n+1}=\frac{x_np(x_n)}{q(x_n)}$$
for $n\ge0$. Find all $n$ such that $x_n=1995$.