  We are looking for integer sets that resemble classical Cantor set and
investigate the structure of their sum sets. Especially we investigate $FS(B)$
the subset sum of sequence type $B=\{\lfloor p^n\alpha\rfloor\}^\infty_{n=0}$.
When $p=2$, then we prove $FS(B)+FS(B)=\N$ by analogy with the Cantor set, and
some structure theorem for $p>2$
