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

0,3

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).

Links

Table of n, a(n) for n=0..56.

Richard Laver, On the Algebra of Elementary Embeddings of a Rank into Itself, Advances in Mathematics 110, p. 334, 1995

Wikipedia, Laver table

Example

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).

Crossrefs

Sequence in context: A265560 A265544 A290221 * A296613 A062383 A034583

Adjacent sequences: A098817 A098818 A098819 * A098821 A098822 A098823

Keyword

nonn

Author

Christian Schroeder, Oct 08 2004

Extensions

More terms from Adam P. Goucher, Dec 18 2013

Status

approved