A Statistical Estimate for the number of times you can divide an even by 2 until it becomes odd

Question

I was wondering if exists function n(m) (where m is an even number) that can give an unbiased estimate for the number of divisions by 2 for even number m until it becomes odd

Answer 1

For a finite sequence of even numbers, all of them will be divisible by 2 once, 1/2 of them will be divisible by 2 twice, 1/4 will be divisible by 2 thrice, 1/8 will be divisible by 2 four times, etc, so you could use the constant function:

$$n(m) = 1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \frac{1}{32} + \frac{1}{64} + ... = 2$$

If you want an upper bound for the number of divisions by 2, then

$$n(m) = \log_2 m$$