Problem solving with programming: Forming the nth binary sequence

Problem solving with programming: Forming the nth binary sequence

A binary sequence contains 0 and 1 only
 
S.No  Binary sequence
--------------------
1     0
2     1
3     00
4     01
5     10
...
Given a number k, we have to design an algorithm to print k^th binary sequence.

Initial approach (not efficient):
 
Starting from the sequence 0, this algorithm iterates k times. 

To get the next sequence, in each iteration we do the following.
 check the last index of 0 in the number

• If it is found change that to 1 and all the digits after that to 0
• If it is not found, the next sequence contains all 0 which is one  digit longer than previous

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