With the big amount of websites that require a registration or provide a benefit for registering, it is impossible to device and remember a unique password for every account we have. A possible solution is the password manager. However, is there a way to generate passwords that don't have to be remembered, but instead can easily be retrieved as needed, without the use of a separate program?
My direction of thought is the following: device a core password (with a backup for those "not more than 16 chars" situations). Use a preselected component of the website - for example, the site name, taking the core password "password", and using the letters of "yahoo" to form the yahoo password, "ypasswordo". Of course, this is not optimal, as website URLs change, especially those of less-used websites, which are incidentally exactly the ones I'm likely to eventually stop visiting and forget the passwords for.
Is there anything I can use from any website I'm registering on that I can be certain will not be changed after a while, and will be different from site to site?
EDIT: Since my question seems unclear, I'll give an example. Imagine that all websites ever created had an ID buried in their source code. It doesn't have to be unique, it just needs to be unlikely to ever change and to be present in all, or at least the vast majority. One could run a simple algorithm on that ID and add a core password to produce a password for that account, which could just as easily be obtained 10 years later just by knowing the algorithm. Is there a part of a website that is unlikely to change, isn't the same across every website out there (overlap is normal, as long as it doesn't lead to rotating 5 same passwords across all accounts)? Is there any way to create and later retrieve a password, doesn't have to depend on the website's code at all, with minimal risk of loss and without any memorization?
TL;DR: Suggest a method that, without extra memorization or program usage, can be used on any random website to produce the used password with complete certainty, or at least a list of up to 10 passwords of which one will 100% be true. The password produced shouldn't be the same across all websites and should have minimal or no risk of being lost, even years after account creation. The end result should be the ability to reproduce the password used on any long-dormant throwaway account from any computer, without dependance on installed programs or online password managers or carrying around the passwords. The passwords don't have to be crazy secure, just reasonably unique.