Digital representations using the greatest integer function

LetSd(α){S_d}(\alpha )denote the set of all integers which can be expressed in the form∑εi[αi]\sum {{\varepsilon _i}[{\alpha ^i}]}, withεi∈{0,…,d−1}{\varepsilon _i} \in \{ 0, \ldots ,d - 1\}, whered≥2d \geq 2is an integer andα≥1\alpha \geq 1is real, and letId{I_d}denote the set ofα\alphaso thatSd(α)... View More