How should I read and interpret $A = \{\,n^2 + 2 \mid n \in \mathbb{Z} \text{ is an odd integer}\,\}$ As my question states, I need to interpret: $A = \{\,n^2 + 2 \mid n  \in \mathbb{Z} \text{ is an odd integer}\,\}$
Does this mean that any odd integer $n$ will work, or does this mean that the output of $n^2 + 2$ must be an odd integer?
For example, would these numbers be in the set: $\{1,3,5,7,\ldots\}$ or would $5$ not be in the set because $2^2 + 2 = 6$? 

It means that $n$ is an odd integer, not that $n^2+2$ is an odd integer. Coincidentally, the set of $n$ such that $n^2+2$ is odd is actually just the set of odd integers, so it makes no difference.
The set in question is
$$\left\{3,11,27,51, \,\,\dots\,\right\}$$
