Feb. 23, 2012
Shalom Doron,
Rosh Chodesh Adar Tov!
I think the reason for the 2, 3, 5, and 8 year gaps may have something to do with the fact that these are the first 4 gaps between Jewish leap years. Without the leap year correction, it's much harder for the two calendars to coincide, even over an 8 day holiday. For example, the annual loss of 11 (or gain of 19) days makes it impossible for Chanukah to include any fixed Roman date in consecutive years. Two years apart, however, is possible if a leap year (and some other things) falls in between, because the loss of 22 days is offset by a gain of 30, a net of 8. Three Years is of course possible because the dates will always be roughly 3 days apart. But then Four years is impossible, etc... Of course to prove your observation one would have to be very careful with difficult calendar minutae.
Steve