Mathematical notation for a function that returns reals but I want to return the integers

Question

How can I modify this notation to denote the following? I want to describe a alternating series generated by taking sin(n) and filtering out all but the integers so that if the domain is R, the resulting series is {1,0,-1,1,0,-1...} .

Answer 1

It's common to put a condition under the sum to denote the $n$'s to be used in the summation so you could write something along the lines of:

$$\sum_{n \in \mathbb{R} \text{ and }\sin(n) \in \mathbb{Z}} \sin(n).$$

Not sure if this is what you're going after?