ZMap: Single packet network scanner designed for Internet-wide network surveys
zmap.io
zmap.io
I'll warn you that even with a list, depending on which ports you scan you're still likely to get abuse complaints. Also port scanning can max out networking bandwidth, and most hosts aren't too keen on either.
[0] https://github.com/zmappingborg/blacklists/blob/master/black...
Sounds like a great way to broadcast your box is interesting.
Sometimes obscurity is a good thing.