MathDB

Let

m

be a positive integer and

\{a_n\}_{n\geq 0}

be a sequence given by

a_0 = a \in \mathbb N

, and

a_{n+1} = \begin{cases} \displaystyle \frac{a_n}2 & \textrm { if } a_n \equiv 0 \pmod 2, \\ a_n + m & \textrm{ otherwise. } \end{cases}

Find all values of

a

such that the sequence is periodical (starting from the beginning).

Problem Statement