Definition
Let $a_n$ be a real sequence.
Assume there exists a continuous real-periodic function $f(x)$ such that
$f(n) = a_n$
And $f(x)$ has the period $t$ , where $t$ is An irrational real number.
Then we say $a_n$ is periodic and has An irrational period. Or we say $a_n$ Has An irrational periodic orbit.
Let $a_0 = \ln(2)$ and $a_{n+1} = (e+1) a_n (1 - a_n)$.
Does there exist an $f$ such that :
$$a_n = f( a + b c^n)$$
Where $a,b,c$ are (fixed) real values and $f$ is a real-continuous periodic function with real irrational period $t$ ?