Representations

With $\alpha$ being a positive real number, what is the smallest natural number that cannot be represented by the two sequences below?

Sequence 1: $\lfloor 1 + 1/ \alpha \rfloor , \lfloor 2 + 2/ \alpha \rfloor , ... , \lfloor n + n/ \alpha \rfloor ,...$

Sequence 2: $\lfloor 1 + \alpha \rfloor , \lfloor 2 + 2 \alpha \rfloor , \lfloor 3 + 3 \alpha \rfloor ,..., \lfloor n + n \alpha \rfloor ,...$

If there is no such number, then enter -1000.