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 \(p>2\)

On arithmetic sums of Cantor-type sequences of integers