KöMaL 2008 B4115

For what positive integers $k$ does 1 occur as a term of the sequence ($a_n$), given that $a_1$=$k$ and $a_{n+1}=\frac{a_n}{2}$ if $a_n$ is even, and $a_{n+1}$=$a_n$+5 if $a_n$ is odd?