Let $A$ be the following.

A numerical sequence is defined by the conditions: $a_{1}=1, a_{n+1}=a_{n}+\left[\sqrt{a_{n}}\right]$.

How many perfect squares occur among the first terms of this sequence, not exceeding

1000000?
According to the solution of problem $\underline{9152}$, all perfect squares in this sequence have the form $4^{m}$. There are exactly 10 numbers of this form within the specified limits

$\left(4^{10}=1024^{2}>10^{6}\right)$.