The atomic numbers are just the quantity of protons which are obviously just positive integers (whole numbers, 1, 2,3, you can’t get 1.255 protons)
In fact your point is why the Periodic Table was so significant because before we arranged elements like this we *were* missing elements and didn’t know it! For example, the 1st periodic table didn’t have the noble gasses at all (we didn’t know they existed).
But some people sat down and say, Wait? Why are missing elements? And they went out and discovered them!
It’s totally possible we’ll find gaps as we discover new elements, but that doesn’t mean they don’t exist, we’ll leave a spot for them as we know they *must* exist, we just haven’t discovered them yet!
EDIT – as u/ComradeMicha has pointed out the largest elements are highly unstable and not found in nature, we can only create them for fractions of a moment within laboratory settings before they decay (break apart). There is a idea of something called “The Island of Stability” where we might discover (read: create in a lab) super heavy elements that *are* stable without decaying, but we haven’t discovered any yet.
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