A098820 Periodicity of entries in the first row of a Laver Table of size 2^n.

1, 1, 2, 4, 4, 8, 8, 8, 8, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16

Offset: 0

Author

Christian Schroeder, Oct 08 2004

Keywords

• nonn

Comments

All sequence elements are powers of 2. The first n for which a(n)=32 is at least A(9,A(8,A(8,255))), where A denotes the Ackermann function (R. Dougherty). If a rank-into-rank exists, then the sequence is diverging (R. Laver).

Examples

			a(4)=4 because the entries in the first row of the Laver table of size 4^2=16 are 2,12,14,16,2,12,14,16,2,12,14,16,2,12,14,16 (and thus repeat with a periodicity of 4).
		

Links

• Richard Laver, On the Algebra of Elementary Embeddings of a Rank into Itself, arXiv:math/9204204 [math.LO], 1992; Advances in Mathematics 110, p. 334, 1995
• Wikipedia, Laver table

Extensions

More terms from Adam P. Goucher, Dec 18 2013