2023 Fermat Problem 15

A sequence has 101 terms, each of which is a positive integer. If a term, n, is even, the next term is equal to \frac{1}{2}n + 1. If a term, n, is odd, the next term is equal to \frac{1}{2}(n+1). For example, if the first term is 7, then the second term is 4 and the third term is 3. If the first term is 16, the 101st term is

\textbf{(A)}\ 1\quad \textbf{(B)}\ 2\quad \textbf{(C)}\ 3\quad \textbf{(D)}\ 4\quad \textbf{(E)}\ 5

If there are no answer choices shown, enter a numerical answer.

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