How were these 7 lists generated?

The first number of each is 1, 2, 4, 8, 16, 32, and 64. The lists are part of a number game where a person thinks of a number and tells you if their number is on each of the cards. If the number is on one, you add the first number of the card. Here's the set of lists.

I don't understand how the lists themselves were made. I can see certain patterns in each, but how were those patterns decided on? Thanks in advance.