User blog comment:MilkyWay90/Not-Registered Users, tell your Googology ideas in the comments/@comment-2601:142:2:EC49:247C:A73D:AD4A:5ED9-20180803125948/@comment-30754445-20180806200135

"if you identify the pattern in this, you can make a rule..."

You can make other rules as well, and.get a different limit.

For example, with the exception of <0,n>,  corresponds to ordinal ω [the k-th hyper operator] w. Depending on how we define hyperoperators for ordinals, this could get you to either ε₀, φ(ω,0) or φ(ω,0,0).