Laver Table - Definition

Definition

For a given a natural number n, one can define the n-th Laver table (with 2n rows and columns) by setting

where p denotes the row and q denotes the column of the entry. Define

and then calculate the remaining entries of each row from the m-th to the first using the equation

The resulting table is then called the n-th Laver table; for example, for n = 2, we have:

	1	2	3	4
1	2	4	2	4
2	3	4	3	4
3	4	4	4	4
4	1	2	3	4

There is no known closed-form expression to calculate the entries of a Laver table directly, and it is in fact suspected that such a formula does not exist.

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