Doing this with server side scripting is crazy.

Porting the exact behavior of a command line application to a GUI environment like a web page is crazy. Reorganizing the content into a form that fits a new environment makes more sense. For example, the questions to test understanding of awesome sequences can all be part of one form, like in my javascript implementation.

You'd have to submit a zillion forms and take a second to get the answer for each try.

By "a zillion", do you mean "tens of"? And a second for the form is a lot shorter than the infinite time it takes on a browser that does not support scripting.

This is precisely the sort of thing client-side scripting is meant for.

No, this is precisely the sort of thing client-side scripting is meant to do better on browsers that support it, without interfering with the good enough implementation on browsers that don't. It most definitely is not meant for the sole means of delivering content that is intended for a wide audience.

Of course, the page would explain that it needed JavaScript, if you had JavaScript disabled, not just show a blank page.

I know I get annoyed quickly when I am asked to enable JavaScript for a purpose that should not need it. It would be better if we could explain that the page will be more responsive with JavaScript.