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I have been out of the sciences for quite some time, but as I do rember there are quite a few elements that are not found on earth. Rare earth elements is what comes to mind. The thing is if these elements ever did exist they would have decayed.
It might not naturally exist here on Earth but that does not mean it cannot exist elsewhere.
NOVA- Island of Stability (transcript and video at the link)
There are two areas that I find quite exciting. One is the continuation of the work that we have performed for about 15 years in collaboration with our colleagues at the Flerov Laboratory of Nuclear Reactions in Dubna, Russia, using an isotope separator connected to their cyclotron to collect rare isotopes and isolate them from the vast amount of unwanted reaction products. The second is a new project, again in collaboration with our Russian friends, in which we are performing chemistry experiments in hopes of determining the detailed chemical properties of the elements we are making.
We have recently made an attempt to produce element 118; we hope that the results of this experiment will help lay the issue to rest.