User blog comment:Primussupremus/more depth in the expansions and theory of my array notation part 2./@comment-30754445-20170518192340/@comment-30754445-20170522094216

Look again at your blog post. You've explicitly written there:

"if d=1, {a,b,c|d} = {a,b,c}"

If you prefer the base case to be d=0, that's fine. But you must be consistent about it, if you want your notation to be well-defined. It can be either 0 or 1, but it can't be both.

Also, the next number in the sequence is not 3 [3^27 arrows] 3. It's close, but not quite. Let's try this one, a single step at time (I assume, for now, that {a,b,c|1} = {a,b,c}):

1. If {3,4,3 | 2} = {3,b,3} then what is the value of b?

2. If {3,b,3} is converted to arrow notation, how many arrows will there be between the 3's?

(I realize that me insisting that you do this 100% right is pretty annoying, but believe me: if you don't practice this careful approach now, you'll get completely lost very quickly)