33. Let $n$ be a positive integer. We define
$$T(n)=\left\{\begin{array}{ll} n / 2 & \text { if } n \text { is even } \\ (3 n+1) / 2 & \text { if } n \text { is odd } \end{array}\right.$$

We then form the sequence obtained by iterating $T$; $n, T(n), T(T(n)), T(T(T(n))), \ldots$. For instance, starting with $n=7$ we have $7,11,17,26,13,20,10,5,8,4,2,1,2,1,2,1 \ldots$. A well-known conjecture, sometimes called the Collatz conjecture, asserts that the sequence obtained by iterating $T$ always reaches the integer 1 no matter which positive integer $n$ begins the sequence.
a) Find the sequence obtained by iterating $T$ starting with $n=29$.
b) Show that the sequence obtained by iterating $T$ starting with $n=\left(2^{k}-1\right) / 3$, where $k$ is an even positive integer, $k>1$, always reaches the integer 1 .