Such a home work assignment should immediately trigger the term 'recursion'. The best way to impress your teacher is: 
perl -E'sub _{push@_,say@_;&_}_'

[download]
It even starts with 0 1's, for extra credits.

If you want to golf, you might want to try 

perl -E'{$_.=say;redo}'

[download]

In reply to Re: Generate the perl sequence 1, 11, 111, .... by JavaFan
in thread Generate the perl sequence 1, 11, 111, .... by alih110

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