# 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 $$a(k)$$.

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