Skew Binary |

When a number is expressed in decimal, the *k*-th digit represents a multiple
of 10^{k}. (Digits are
numbered from right to left, where the least significant digit is number 0.)
For example,

When a number is expressed in binary, the *k*-th digit represents a multiple of
2^{k}. For example,

In **skew binary**, the *k*-th digit represents a multiple of
2^{k+1} - 1.
The only possible digits are 0 and
1, except that the least-significant nonzero digit can be a 2. For example,

The first 10 numbers in skew binary are 0, 1, 2, 10, 11, 12, 20, 100, 101, and 102. (Skew binary is useful in some applications because it is possible to add 1 with at most one carry. However, this has nothing to do with the current problem.)

10120 200000000000000000000000000000 10 1000000000000000000000000000000 11 100 11111000001110000101101102000 0

44 2147483646 3 2147483647 4 7 1041110737