How do I calculate the position of a minimum number(?) of equal sized spheres so as one of the spheres is laterally unobservable at the center (unable to see it from any chosen lateral side but still able to see it from either top or bottom), without the spheres touching one another, all the while considering distance proportionate to size?

If they were able to touch one another it would be six spheres to obstruct the one.

If they were able to touch one another it would be six spheres to obstruct the one.

I'm sorry, but I don't understand the question. If you had 6 touching spheres arranged around a central sphere, you would still be able to see that central sphere because the 6 exterior spheres touch each other at only one point, so from the outside you could still see above and below the point where they touch to see the central sphere. Am I missing something? Perhaps you could have two rings of exterior spheres, arranged so that the view between any two adjacent spheres on one ring is obscured by a sphere on the other ring? Just a thought...