MathDB

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

\lfloor x\rfloor

denotes the greatest integer less than or equal to

x

. For each

k

find the set

A_{k}

containing all integer values of the sequence

(\sqrt[k]{a_{n}})_{n\geq 0}

Problem Statement