Chemistry - Why were elements discovered "out of order" after 1950?

Solution 1:

The synthetic trans-uranic elements (the "modern era" elements as you call them) are synthesized by bombarding a certain isotope of one element with a certain isotope of another element with a lot of energy in order to get nuclear fusion. The reason they are "out of order" is that the building blocks of these elements have to be very specific isotopes (extra rich in neutrons for example, somewhat abundant for another). This limits the possible sources considerably and so the heavy elements synthesized (and hence discovered) earlier were those where there was a convenient pair of smaller elements to combine to form the larger ones. You don't just bombard each successive element with protons to make the next one.

A lot of the early discoveries were made by bombarding sources with alpha particles, so there are several discoveries that are increases by 2 protons (e.g. Cm->Cf, Am->Bk). Indeed, the table you linked gives more examples of the pairs of elements used to make the heavy actinides and beyond.

Solution 2:

The major reason is arguably nothing to do with chemistry (unless you count nuclear physics as nuclear chemistry).

The big issue is that nuclear stability isn't linear with atomic number. Some configurations of protons and neutrons are more stable than others (for reasons that would require quite a lot of nuclear physics to explain). Nuclei with even numbers of both protons and neutrons tend to be more stable, for example. There are particular magic numbers of both that impart some extra stability. And Nuclei containing odd numbers of protons and even numbers of neutrons are less stable than nuclei containing even numbers of protons and odd numbers of neutrons.

The basic takeaway of these observations is that the stability doesn't change in a simple fashion with atomic number (the number of protons). Nuclei with odd numbers tend to be less stable, for example. This means that the easiest ones to make are sometimes not the next element but the next but one element. Or something beyond that. There is even a theory that says there is an island of stability where we will discover some unusually stable heavy elements somewhere slightly beyond the list we currently have.

So there is not reason to expect that we should discover new elements in the order of atomic number.

More detail here.