PARI/GP practice #2

Define the Collatz function $c(n)$ as follows: if $n$ is even, then $c(n)=\frac{n}{2}$ . If it is odd, then $c(n)=3n+1$ . Let $a(n)$ be the least number of applications of the function $c$ on $n$ that is equal to $1$ . (For example, $a(3)=8$ since 3 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1 has length 8, and $a(12)=10$ since 12 -> 6 -> 3 ->... -> 1 has length 10.) Let $k$ be the concatenation of all positive integers up to and including $1000$ (starts $12345...$ ). Find $a(k)$ .