User blog comment:Mh314159/Help me understand a natural number recursion/@comment-39541634-20191016190652/@comment-39541634-20191017035153

No problem. Glad I could help.

Also, I've just written a computer program that calculates g and f (as long as they don't get too large). Indeed, f(512,x) is 4x+1.

So either there's some mistake in the definition, or CatIsFluffy meant another number when he said 512.

I also tried to analyze the function on paper, and couldn't make heads or tails of it. It can, indeed, be converted to a sort of array notation (we get there by defining [a,b]=2^a*(4b+2) and =[a,b]-1) but the end result doesn't ring any bells. I wonder how Cat arrived at these rules in the first place, because the behavior is quite complex yet it doesn't resemble any ordinal notation I know.

If Cat is reading this, I'll appreciate any explanation as to how this function is supposed to work. How is it supposed to reach TREE (and - I presume - the BHO as well)? What's the rationale behind the expansion rules?

Quite interesting.