Looking at the get_terms function definition, the value for name__like will be passed to the SQL query like:
" AND t.name LIKE '{$name__like}%'"
As such, I believe that you can only search for one of the numbers.
As an alternative strategy, you could iterate over the numbers you want to pull from the database:
$terms = array();
$numbers = range( 1, 6 );
foreach ( $numbers as $number )
$terms[] = get_terms( 'movies', array( 'name__like' => $number ) );
As yet another alternative, you could make all of these terms that you want to get a child of another term. For instance, if you make a parent term called “Numbers”, with id of 5, and assign all of the “numbered” terms as a child of this term, you could do:
get_terms( 'movies', array( 'parent' => 5 ) );
Obviously, the success of either strategy is dependent upon your use case. The first alternative is rather expensive, but with a nice caching strategy really shouldn’t be an issue. The second method requires structuring data differently that may or may not work for your situation.