  We define a class of sequences ${a_n}$ by $a_1=a$ and $a_{n+1}=P(a_n)$, where
$P(x)$ is a polynomial with real coefficients. We then find out for which
values $a$ and for which polynomials $P(x)$ these sequences will be constant
after a certain rank. Then we generalize it from polynomials $P(x)$ to real
functions $f(x)$.
