Ok, got a new answer..
It appears that ...
the first number in each set is just the computer counting by 1s, but you've mixed up the least significant bit with the most significant bit..
That is the first number in each set is ...
'3' --> decimal 51 --> binary 00110011
'³' --> decimal 179 --> binary 10110011
's' --> decimal 115 --> binary 01110011
etc..
So the next three sets (after the final no_output that was added to the question later) will start with ...
binary 00101011 --> decimal 43 --> '+'
binary 10101011 --> decimal 171 --> '«'
binary 01101011 --> decimal 107 --> 'k'
Therefore the next three patterns are:
+$*.
«¤ª®
kdjn
Hope I did those conversions right.. I feel better about this answer than my previous one.