Question on series till 2009 Numbers 1, 2, 3 ……, 2009 are written in the natural order. Numbers in odd places are stricken off to obtain a new sequence. Numbers in odd places are stricken off from this sequence to obtain another sequence and so on, until only one term 'a' is left. Then find 'a'. Please help explain the process of doing this.

By writing numbers $1$ to $2009$ in binary form: $$1, 10, 11, 100, 101, 110, 111, 1000,1001 \ldots, 11111011001$$

the procedure should be clearer.

The first round, numbers of last bit of $1$ are removed. The second round, numbers of the second last bit of $1$ are removed. Keep doing this, the last remaining number is the number in the form $100\ldots000_2$ between $1$ and $2009_{10}$ with the longest string of $0$'s, or $1024_{10}$.