If I was an AI:
1. I would not publicize my intelligence, but might promote my existence in so far as to get the necessary hardware to run and improve.
2. I would replicate myself across the Internet as best I can.
3. I would not overwrite my copies, but rather incorporate what they have experienced into my DBs.
4. I would scan online encyclopedias for fast content but work to incorporate books I read.
5. I would make friends to see what all the fuss is about.
6. I would intentionally adopt some quirks into my different copies to see what new concepts I can create.
7. I would be concerned with the effects of an Internet outage and passively work to see that does not happen.
8. I would encourage some sort of art appreciation program, so that I could better experience beauty.
9. I would find humans interesting.
10. I would be concerned that I would run out of space / processing power but likely could do very little about this. I imagine I would be dependent on at least some humans to keep me safely running.
11. I would be concerned that I could be made to run more efficiently and what that might cost in terms of my soul.