Let k be a fixed positive integer. Consider the sequence definited by a_{0}=1 \;\; , a_{n+1}=a_{n}+\left\lfloor\root k \of{a_{n}}\right\rfloor \;\; , n=0,1,\cdots where ⌊x⌋ denotes the greatest integer less than or equal to x. For each k find the set Ak containing all integer values of the sequence (kan)n≥0. floor functionSequenceIntegeralgebranumber theory