Is it possible to construct a set of numbers of arbitrary size such that any calculation involving addition and subtraction, on any combination of those numbers, produces a unique result?


For example, the set of numbers 1,2,3,4,5 would not satisfy this condition because:


* 1 + 2 = 3
* 1 + 5 = 2 + 4 = 6
* 1 + 2 = 5 - 2 = 3


I'm writing some code that performs calculations on a set of numbers, and I want to set up some default data to perform unit tests on my code. I would like to ensure that all calculations produce a unique result to avoid having any false positives in my tests.


For my case, I need a set of 22 numbers.


This is my first question on mathoverflow. If I've done anything incorrectly, please let me know.



Set of number with unique sums of elements
Taking different powers of 3, i.e. 
1,3,9,27,81,... should do the job.


