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A098820 Periodicity of entries in the first row of a Laver Table of size 2^n. 0


%S 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,

%T 16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,

%U 16,16,16,16,16,16,16,16

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

%C 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).

%H Richard Laver, <a href="http://arxiv.org/pdf/math/9204204v1">On the Algebra of Elementary Embeddings of a Rank into Itself</a>, Advances in Mathematics 110, p. 334, 1995

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Laver_table">Laver table</a>

%e 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).

%K nonn

%O 0,3

%A _Christian Schroeder_, Oct 08 2004

%E More terms from _Adam P. Goucher_, Dec 18 2013

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Last modified September 27 13:13 EDT 2020. Contains 337380 sequences. (Running on oeis4.)