[Tutor] Recursive list checking

[joe_schmoe]

Dear Pythonites

I am looking for a more elegant solution to a piece of code that is too 
unwieldy and reptitive. The purpose of the code is for a new addition to 
a list to check whether it is a duplicate of a list element already a 
member of that list, and if so to regenerate itself randomly and to 
perform the same check again until such time as it is unique.
For example, this is what I am currently doing:

=============code block ========================

    # generate unique numbers and append to list
    nmbr01 = random.randrange( 1, 20 )
    nmbr_list.append( nmbr01 )

    nmbr02 = random.randrange( 1, 20 )
    # check for duplicates and re-generate a number if needed
    while nmbr02 in nmbr_list:
        nmbr02 = random.randrange( 1, 20 )
    nmbr_list.append( nmbr02 )

    nmbr03 = random.randrange( 1, 20 )
    while nmbr03 in nmbr_list:
        nmbr03 = random.randrange( 1, 20 )
    nmbr.append( nmbr03 )

================================================

This method works, but increasing the numbers to be appended makes the 
code excessively long. I can't see anything in list methods that seems 
to do the trick, so anybody want to make a suggestion please?

TIA
/j