The following were calculated with various incarnations of my conjunction program.
This run was made during 2015 (on a Mac):
The SEPARATION column is geocentric for the conjunctions in ecliptic longitude. The distance of the planetary centers is shown. The SIN RM column helps to convert this to the closest approach distance. Then the parallax shift is considered for the best viewing location on Earth to yield a maximum overlap. If this overlap has a positive value an occultation is flagged.
I'm presently assessing the accuracy of this run. For example, it's possible the positions of Mercury (perhaps more than most) can drift a few arcseconds over the 2000 year integration. It's interesting that the upcoming MERCURY NEPTUNE occultation in 2067 is a rare event with a recurrence only around every 2000 years. I'm experimenting with some even longer runs and I'm starting to find some Jupiter-Saturn occultations in the distant past with the most recent more than 8000 years ago in 6858 BC. The next Jupiter-Saturn occultation happens in the year 7541 with two happening that year!
These are geocentric conjunctions (run on a UNIX system in 2003):
These are geocentric conjunctions listed for closest approach:
The December 2020 Jupiter-Saturn conjunction, passing within 6 arc minutes is the closest one in about 400 years. The 1623 conjunction happened too close to the sun in the sky to easily see. The last time an observable conjunction happened at least as close was in 1226, when Jupiter was only 2 arc minutes away from Saturn. There is a fairly regular cycle of around 400 years passing between Jupiter-Saturn conjunctions closer than 0.1 degree, though in 2080 they pass barely over 0.1 degree apart.
These are geocentric conjunctions in ecliptic longitude (VAX version run around 1994):
These are three-planet conjunctions when the planets fit in the smallest circle:
Additional information on these calculations is found in "Mutual Occultations of Planets: 1557-2230", Sky and Telescope, March 1979.
There was a remarkable coincidence that the printed version of the Sky and Telescope article appeared on the same page as an article about Galileo and his lunar drawings. My article also suggested examination of historical observations to see if Uranus or Neptune could have been mistaken for a moon of Jupiter and thus being seen before it was discovered. Charles Kowal and Stillman Drake followed up on that notion using Galileo's observations from 1613. It turns out that Neptune actually shows up as a moving "star" on Galileo's drawings so Galileo himself unwittingly observed Neptune right around the time of the invention of the telescope. This was published in Nature and Scientific American in 1980. My role in this was recognized in receiving the R.R. Newton award by the International Journal of the Scientific History in 2009, and further discussed in 2015.
Some additional occultations were found by Larry Bogan on his website. Occultations from -2000 to +3000 were posted by Shinobu Takesako in 2016.