We typically learn binary system, hex system in our courses. Most of them are predictable in their position values or they are linear. This system is not linear as its dependant on Fibonacci series.
3 is the first duplicate (ignoring 1 as we started with 1). We can represent 3 as 100 or as 011.From there you have many duplicate representations. There are some numbers which can be represented only one way.
If you find that sequence please let me know. Those numbers are also interesting