What is the underlying pattern, or algorithm(s) used in these numbers?
11 instances of data is insufficient for discovering the behavior (even finding patterns) for such presumably complex systems. You need at least thousands of them.
These numbers are encoded versions of numbers generated by Serial Key Generation Algorithms, which in my experience are usually implemented by Python. So it's not at all strange that there may be a correlation between some digits of them. As it is necessary for the system to recognize its created numbers from the numbers created by other lotteries.
Even if there was a correlation or correlation between all the instances of lottery numbers, correlation doesn't imply causation and these patterns, if found any, couldn't really give any information about the key generation system itself.
If you are really serious about it. you could go to this page and enter your data as a sequence it would show you the pattern, if there is any:
The On-Line Encyclopedia of Integer Sequences