Task 2. Find the number of natural numbers not exceeding 2022 and not belonging to either the arithmetic progression $1,3,5, \ldots$ or the arithmetic progression $1,4,7, \ldots$
Answer: 674.

Solution. These two progressions define numbers of the form $1+2n$ and $1+3n$. This indicates that the desired numbers are of the form $6n$ and $6n-4, n \in \mathbb{N}$. Since 2022 is divisible by 6, the numbers of the form $6n$ will be $\frac{2022}{6}=337$, and there will be as many numbers of the form $6n-4$. Therefore, the total number of numbers is $337 \cdot 2=674$.