Create a formule for placing points on places where are no points

I have a dataset with coordinates from all letterboxes in a certain area. I want to have all the letterboxes in a maximum of 500m away for everyone. So if there is a place without a letterbox nearby, I want to place there a letterbox (or more than one if it is needed).

Does anyone know a formule to get the coordinates of the places where a new letterbox is needed?