Useful Uspensky

2020,α,β,4040,2α,2β,6060,3α,3β,2020, \lfloor \alpha \rfloor, \lfloor \beta \rfloor, 4040, \lfloor 2\alpha \rfloor, \lfloor 2\beta\rfloor, 6060, \lfloor 3\alpha \rfloor, \lfloor 3\beta\rfloor, \dots

Do there exist two positive real numbers α\alpha and β\beta, such that each positive integer appears exactly once in the sequence above?


This problem is from Korea 2020 Math Contest.

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