Simple password generating idea

I think I've come up with a way to generate passwords for whatever web sites, programs and other such things, even for ATM (whatever number of digits). I wanted something I didn't need to write down (easy to remember) and that I could figure out in my head, (under five minutes).
The basic idea is to have a master password that I remember and a formula that works on that password and the 'name' of whatever it's for. The only thing I'd have to write down is what number change it is as I'd be changing them regularly. This could be done to a synchronized file on my cellphone, iMac, iPad and whatever else I have. I could also include in this file the name of the website, program or whatever that the main password and formula would work on. So basically I would have to figure out in my head (if I forget the answer ) what {main password + formula + name of website + number of change} = {password} .. The answer should be the same every time I do it, and if I'm smart enough I should be able to figure it out in a couple of minutes. The first time I do it I should remember the password or at least try to.
What down sides can you see in this idea? I assume people have tried similar attempts, is there a name for it?

Yes - useless.

Why not just remember the passwords you need to? If for some reason you are unable to remember them, you've got a problem.

Best regards,
AstroTux.