You've answered your own question by posting an image of the Periodic Table - clearly there are no gaps between 1 and 118.
However, since this is WB and not Physics, let's speculate. The nucleus is usually depicted as a bunch of grapes, forming a spherical structure, since that is the lowest energy state. But is it...
Nuclei are bound together by the Strong Force. This is very short range - essentially binding nucleons to their nearest neighbours. Fighting against the Strong Force is the electrostatic repulsion of the protons, which is long range. Any one proton feels repelled by all the others in the nucleus. As the nucleus grows, the repulsive force becomes greater while the Strong Force doesn't really change. Adding neutral neutrons helps because this pushes the protons further apart, thus weakening the electrostatic force. 969
This is why the proton-neutron mix starts off about equal and becomes increasingly neutron-rich as we go up. By the time we get to a few hundred nucleons, it is getting difficult to keep the thing together and we get radioactive isotopes that keep falling apart.
However, what if there is a region of stability in the very large atomic number range? Maybe when we get to, say, 1000 nuclei, structures can form that lead to it being stable. For example, you could have an outer shell of alternating protons and neutrons (like the pattern on a football) with a central core of neutrons. That would keep the protons well apart but allow you to have a massive nucleus.
Its chemical properties would be weird - a giant nucleus would play havoc with the electron orbital radii. It would be very dense - maybe two or three orders of magnitude denser than existing elements. If you perturbed the proton-neutron lattice, it would decay into a spray of lighter elements and release rather a lot of energy, I would imagine.
Such a thing would be unlikely to form naturally since nuclei are usually made by squishing together lighter nuclei. However, you might be able to engineer such a nucleus: make a 2D $p-n$ lattice, then wrap it round a blob of neutronium. Simples! 969