User blog comment:TechKon/Left-right arrow notation/@comment-5150073-20150810092730/@comment-28124748-20150810100843

I'm not sure if I can define it formally, but this is the pattern:

a↔b is defined as; b being the number of levels a↑↑..↑↑a is repeated.

Level one is an "a" number of arrows in a↑↑..↑↑a = a↔1

Level two is an "a" number of repeated a↑↑..↑↑a with a↑↑..↑↑a with a↑↑..↑↑a .... with a↑↑..↑↑a with "a" arrows, with an "a" number of "a↑↑..↑↑a"s = a↔2. Similar to the way Graham's number is.

Level three is an "a" number of repeated a↑↑..↑↑a with a↑↑..↑↑a with a↑↑..↑↑a .... with a↑↑..↑↑a with "a" arrows, with an a↑↑..↑↑a with a↑↑..↑↑a with a↑↑..↑↑a .... with a↑↑..↑↑a with "a" arrows, with a↑↑..↑↑a with a↑↑..↑↑a with a↑↑..↑↑a .... with a↑↑..↑↑a with "a" arrows, ....... with a↑↑..↑↑a with a↑↑..↑↑a with a↑↑..↑↑a .... with a↑↑..↑↑a with "a" arrows, with an "a" number of a↑↑..↑↑a with a↑↑..↑↑a with a↑↑..↑↑a .... with a↑↑..↑↑a with "a" arrows = a↔3.

a↔4, a↔5, a↔6

And so on..

a↔b is, simply put, an b-level array of repeated a↑↑..↑↑a's.