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.
Read more about this topic: Laver Table
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