# Can someone explain what these questions are asking?

1. Jan 14, 2008

### rbzima

Let $$a_{0}$$ be any positive integer and let $$a_{k+1}=a_{k}+1$$ if $$a_{k}$$ is odd, and let $$a_{k+1}=a_{k}/2$$ if $$a_{k}$$ is even.

Let $$\ell$$ be the smallest positive integer where $$a_{\ell}$$ = 1. Find an expression for $$\ell$$ in terms of $$a_{0}$$ that is non-recursive.

2. Jan 14, 2008

### LukeD

So, a_0 is given, but arbitrary, and you're trying to find an l for which l > 0 and a_l = 1

For instance if a_0 = 1
Then a_1 = 2, a_2 = 1, so l = 2

If a_0 = 17, then a_1 = 18, a_2 = 9, a_3 = 10, a_4 = 5, a_5 = 6, a_6 = 3, a_7 = 4, a_8 = 2, a_9 = 1
So l = 9

You just want to solve for l in terms of a_0