Unique Number Calculations

Question

What do you call numbers you can add together that will always be unique.

$a = 1,$

$b = 2,$

$c = 4$

Any combination of the above will always result in a unique number. eg:

$7 = abc,$

$6 = bc,$

$3 = ab.$

Sorry if this is a simple maths question, I have tried searching google however I keep coming up short.

Thanks

Answer 1

Many numbers will show this property

But Let's look at powers of $2$

additive combination of $2^0,2^1,2^2,2^3\cdots$ will give you any positive integer you want

And one number from this set is required to use only once (Notice the binary representation of any Integer)

e.g $23_{10}=10111_{2}$ $$1\times2^4+0\times2^3+1\times2^2+1\times2^1+1\times2^0=2^4+2^2+2^1+2^0=23$$