Question 2
Let $a_1,a_2,a_3,\ldots$ be a sequence defined by $a_1=33$ and, for $n\ge1$,
$$a_{n+1}=a_n+\frac1{\left\lfloor a_n+\frac12\right\rfloor}.$$
Which integers appear in the sequence?
$$a_{n+1}=a_n+\frac1{\left\lfloor a_n+\frac12\right\rfloor}.$$
Which integers appear in the sequence?