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Q: Proof of the uniqueness of the 4-2-1 loop in the Collatz 3x+1 map?

Gianmarco FabbrisA $k$-special $3$-smooth representation (sequence A213539 in the OEIS) is defined as any integer that can be written as $$\sum_{j=1}^k {3^{k-j}2^{a_j}}$$ for some strictly increasing sequence $a_j$ (meaning that $a_{j-1} < a_{j}$). We call $k$ the level of the representation and we define the ran...

 
 
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