Block subsequence theorem

n(4) 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.

Let A be a version of the Ackermann function, and A(n) = A(n, n). n(4) is lower bounded by AA...A(1), where there are A(187196) A's.

n(1) = 3, n(2) = 11 and n(3) > A(7198, 158386).