What are synthetic radioactive elements?

There are several possibilities for elements that are always radioactive and are artificially produced:

Technetium

Promethium

Any element with atomic number 92 (plutonium) or heavier. There are approx 25 of these in existence up to element 118 (element 117 has not been made yet). Additionally, it could be argued that plutonium is found naturally. But only the faintest traces can be found, and could be said to be produced artificially via neutron capture by uranium. It might be (and probably is) possible to create technitium or promethium in the same manner if precursor nuclei for those elements are found with naturally occurring uranium. Neutron capture is possible across a fairly wide range of elements.