I need to create a set of numbers where any amount of them can be added together and each result will always give a unique answer, so we always know that the result was created from adding exactly these numbers and no other combination in the set can work. I'm not sure how many numbers I will need in the set at this point, so am just looking for a general rule. If someone can give me a name for the concept or something which I can then research myself I'm happy to do this, just struggling to word the problem properly to find an answer myself. Thanks in advance for any help!



Set of numbers with unique results from sums
The term would be "subset sum distinct sets". An initial reference to start with is ["A construction for sets of integers with distinct subset sums"](https://www.combinatorics.org/ojs/index.php/eljc/article/view/v5i1r3) by Tom Bohman.


