Is there any series of games that were released on the PlayStation systems in order?

Star Ocean 1 and 2 are direct sequels. Star Ocean 4 seems to be that way also, with a main character from the Kenny family. Star Ocean 3 had a lot of references to 2 but then it ruins them all. Also Star Ocean 4 was released on the 360 first, and then the PS3. There is no prequel.

Shows how much I've been paying attention to game news lately. Budget and stockpile making me intentionally not look up things anymore so I can avoid temptation.

 Spoiler

Yeah, while the game itself was fun, that plot twist in the middle of 3 made me rage.

But yeah, there are quite a few that go PS1-PS2 and a couple that go PS2-PS3, but not much out there that has spaned all three while remaining a console exclusive.