Graham Array Notation

is a notation made by Googology Wiki user Rpillager. Graham Array Notation Retrieved Aug 27, 2023, intending to make certain numbers expressible with a "nicer-looking" array. It has structure [#] where # is an array. 
== Definition ==
All entries in all arrays using this notation must be nonzero positive integers. An example of a valid array is [3,4,5,6,7].
@ is the rest of the array and can only contain numbers, {}'s (if we go to the extension) and commas (separators).
If an array has 3 or less entries, the rules are exactly the same as 3-entry arrays in BEAF/Bird's array notation.
If an array has 4 or more entries, we set forth the 3 following rules:
Rule 1: [a,1@] = a
Rule 2: [@1] = [@]
Rule 3: when b > 1, [@a,b] = [@[@a,b-1]]
=== Extension ===
Define [a,b{1}2] as [a,a,...,a] with b a's.
Applying rule 3, we can also define [a,b,c{1}2] as [a,[a,b,c-1{1}2]{1}2]. 
Continue and one can arrive at [a,b{1}3] which is [a,a,...,a{1}2] with b a's before the {1}.[a,b{1}c] = [a,a,...,a{1}c-1] with b a's before the {1}.
== Examples ==
G(64) (Graham's number) can be defined as [3,3,4,64]. Decomposing it gives [3,3,[3,3,4,63]], which gives [3,3,[3,3,[3,3,4,62]]] and so on. G(n) = [3,3,4,n]. 
== Issues ==
== References ==
Category:Notations
Category:Functions
Category:Array Notations