## Form o a sequence

Hi

Does anyone know the form of the following sequence:

0,1,0,2,
0,1,0,3,
0,1,0,2,0,1,0,4,
0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,5

(in fact this sequence are the powers of two at integer numbers)
i.e.

$1 = 2^0$
$2 = 2^1$
$3 = 2^0\cdot 3$
$4 = 2^2$
$5 = 2^0\cdot 5$
$6 = 2^1\cdot 3$
...

As far i have found that:
$
A_{2^s(2n+1)}=s
$

However i havent found any relation between $s$ and $n$

Any idea?

Thank you a lot