User blog comment:Googleaarex/N-Goodstein Sequence/@comment-1605058-20131223222451/@comment-5150073-20131224165947

I believe tetration cannot be used in the same manner as the first hyper-operators, since there is no nice way to get the proper rule for X^(X^^X) = X^^(X+1). Much easier would be define X^^(X+1) = (X^^X)^X, i.e. go through weak hyper-operations.