I've found the loop. It seems to be 2, 1, 2, 1, 1, 2, 1, 1.
Thus:
2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, [...] etc.
The speed is 1.375 pixels per frame.
It's pretty tedious to post all the frames that I've tested so instead I'll give them all with difference blend mode (nothing to see there, really, but it's fun anyway):
I'll test if this is the same for jumping later. I only very briefly looked at it with frame advance, but I think that it's slightly different (I'm thinking 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, from what I could see without taking screenshots). I'll do this more accurately later. Looks like you might need to make a bot to calculate when the best time to jump is if you're ever gonna remake Rockman, Bisqwit, since I know I wouldn't want to have to think so much about every single jump. :)