Steps to take from a paper to a patent? My question relates to the following thread I posted some weeks ago:

How to publish a paper that does not seem to be within the scope of any journal?

I have written the paper mentioned in that thread, which I HAVE NOT PUBLISHED YET (see the history there; I was entertaining the idea of uploading it in Arxiv, but right now it seems more reasonable to me to keep calm and do not risk anything in any dumb move which might cost me dearly; there is always time to upload it or publish it later on). 

The thing is: as of late I have received very positive feedback from some mathematicians and / or computer scientists which read the paper I sent them privately. The paper provides some very fruitful clues for further practical implementation which engineers or computer scientists might undertake. I myself could give them the indications to do it, at least at the beginning. It is not far-reaching to think that some application (algorithm, software  and the like) might derive from that. I would like to be legally as assured as it gets, so, the question is twofold, I guess:

Could I patent the basic findings from the paper, without waiting for the specific applications?

Should I necessarily be part of the application in order to economically profit from it, or does any other form suffice (say, the people taking up the task signing their intellectual dependence on the paper or the like?).

I would like to know how to proceed so that the transition is smooth and no one gets busted in the process (neither me nor the others).
What you can and cannot claim in a patent is a highly debated area. You should really consult a legal expert.

If you're affiliated with a college or university, they probably have an office that handles these sorts of things. They'll guide you through the patent process and help cover some/all of the fees. You might not have any choice of working with them. Depending upon your contract, the school might own part of your work and have the legal option to attempt to monetize it first.

If you're not with an organization or you know that you're free from any legal obligations, you should get in touch with a patent lawyer. They can help you draft the patent, help look for prior work, and advise you on the intricacies of international IP. 

You can try to patent it on your own, but I really advise against it. A lawyer will help you understand what parts of your work you can patent. They will also help to draft the patent in as broad a way as possible to allow you to claim as much as you can.