I am going to introduce you to a set of numbers: the Graham numbers. These numbers are calculated by the G function, and some of them can be very big indeed.
Before I begin, I would like to introduce you to the notation in case you aren't familiar with it. G represents factors of the function. G1 is \(3\uparrow\uparrow\uparrow\uparrow3\) while G64 is Graham's number.
The first number is Grahamplex. It is equal to G(G(G(G...64)...) where there are a Graham's number amount of Gs subscripted under the main G.
The next number is Grahamduplex where the amount of Gs is equivalent to the tetration of Graham's number by Graham's number.
The next is Grahamtriplex where the amount of Gs is equivalent to Graham's number and Graham's number separated by a Graham's number of up arrows.
The next is Grahamquadplex with the amount of Gs being equal to Graham's number repeated in Conway Chain notation a Graham's number of times. \(Graham\rightarrow\rightarrow...\rightarrow Graham\)
And so on and so forth!
Edit: There is another number unrelated to the Ackermann series that I would like to discuss: Rayoplex. It has the same definiton as Rayo's number except having googolPLEX symbols or less. It would be written as Rayo (Googolplex).