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In my cut content and tcg inspired headcanon,
Oak would be missing in gen 2, having been kidnapped by team rocket, and replaced with Imposter Oak.
You would start your game getting your pokemon from Blue, his grandson now turned researcher, and a quest to see Mr Pokemon about Oak's probable whereabouts. Mr. Pokemon would then give you his Pokedex and tell you to find Bill, as Oak last said he wanted to see him about upgrading the PC system to store the recently discovered Pokemon Eggs. You would then find Bill and Oak locked in the basement of Bill's lab, which has been trashed by Team Rocket. Oak will tell you that Team Rocket stole the access codes for the update to the PC system and went to the radio tower to broadcast that all trainers should come to the Radio Tower to upgrade their PC system with Oak there, but that would make Rocket able to access the Pokemon PC system of every trainer that came and steal their mons, and you would go there and battle imposter oak and save the day.
