A Laver table for a given integer has rows and columns with each entry being determined thus: , with for the first column. Subsequent rows are calculated with .
For example, is
The entries repeat with a certain periodicity . This periodicity is always a power of 2; the first few periodicities are 1, 1, 2, 4, 4, 8, 8, 8, 8, 16, 16, … (see A098820 in Sloane’s OEIS). The sequence is increasing, and it was proved in 1995 by Richard Laver that under the assumption that there exists a rank-into-rank, it actually tends towards infinity. Nevertheless, it grows extremely slowly; Randall Dougherty showed that the first for which the table entries’ period can possibly be 32 is , where denotes the Ackermann function.
This entry based entirely on a Wikipedia entry from a PlanetMath member.
|Date of creation||2013-03-22 16:26:13|
|Last modified on||2013-03-22 16:26:13|
|Last modified by||PrimeFan (13766)|