N(3)

n(3) is a large number used in Harvey Friedman's Block Subsequence Theorem.

n(k) is defined as the length of the longest possible sequence that can be constructed with a k-letter alphabet such that no block of letters xi,...,x2i is a subsequence of any later block xj,...,x2j.

n(3) is lower bounded by A(7198, 158386) and upper bounded A(A(5)), where A is a version of the Ackermann function and A(n) = A(n, n).

n(1) = 3 and n(2) = 11. n(4) > AA...A, where there are A(187196) A's.