How can I derive a formula that produces a set of numbers per index? For example, assuming I am using the set of natural numbers $\mathbb{N}^* = \mathbb{N} \cup 0$ as my domain.
I want to create an algorithm such that at each index value $i$, I output a set.
For example,

$0$ maps to $\{1,2,3,4\}$
$1$ maps to $\{5,6,7,8\}$
$2$ maps to $\{9,10,11,12\}$

How might I go about deriving the function needed to produce the desired codomain?
Just map $n$ to $\{4n + 1, 4n+2, 4n+3, 4n+4\}$.