Hi, having done a 29 day and a 21 day water fast, and some shorter ones, such 'extreme' ideas are more comprehensible than they would have once been: and I currently (usually) eat only one meal a day, so effectively, am fasting 18-20 out of every 24 hours or so. That is do-able, enjoyable -i like to feel unencumbered- but it could also just as easily be, or lead to, a form of malnourishment. I'm pretty careful that my food 'be my medicine', so for now, it's working.
It IS possible for people to NOT eat anything, extendedly, and thrive, but such situations are rare; you see what I mean. And once food is part of the equation, then food is what we need. I'd like to one day be able to eat very minimally, but do recognize that involves changing the way the body works--and the mind; it's a subject that's outside the scope of this forum.
My concern with your idea would be, that it's difficult to get enough high-density nutrients, by eating on weekends only. Water Fasting is one thing, where the body practises muscle-sparing, etc. and brilliantly manages its altogther intricate hierarchy of healing/sustaining, but calorie-restriction of the sort that you are speaking of would amount to "dieting", aka malnourishment. And I think it might be hard on a body, to go four days into a fast, and then break it, then fast again. . . I'd be more enthusiastic about an extended one day a week fast, i think. Or the one meal a day.
I'm not an expert, but it sounds like it could be more of a feast-and-famine scenario, (which tends to lead one to the thought of a possible eating "disorder".) What do you eat during that non-fasting window? What are your reasons for so much fasting? You can see how your question could give rise to some probing questions in reply.