This is a can of worms, I know.
I was looking at
https://oeis.org/A089047 ... and it seems I was the last to make a big run on it.
For that and other hard problems, I'd like someone else to work on them.
What if I made a $100 prize .... and donated $200 to OEIS? Well, THAT problem is really, really hard to check. So, it's an inappropriate can of worms to foist off onto OEIS.
However ... there are a few hard OEIS sequences that are easy to check. Maybe those would be appropriate for prizes.
So, perhaps the rules would be:
1. Has to be hard to find ... but easy to check.
2. The prize grantor donates 2X to OEIS.