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Graham Array Notation is a notation made by Googology Wiki user Redstonepillager[1], 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[]

  1. Rpillager. Graham Array Notation Retrieved Aug 27, 2023
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