User blog comment:DrCeasium/HAN: better definitions/@comment-5029411-20130704212542

Next Def. is a![1,2n+1] = a![2...1 1,2n] (a 1's), then a![1,21...1,21,2n+1] = a![1,21...1,2[2...1 1],2n] (a 1's).

We define [1]w(*)2/n = [1(*)21...1(*)21(*)22] (a n's). Then [1(n+1)22] = [1]w(*)2/[1]w(*)2/...[1]w(*)2/[1] (a [1]'s).

Next is [1,3n+1] = [1(1)2[2...1 1],3n] (a 1's). In general, [1,m+1n+1] = [1(1)m[2...1 1],m+1n] (a 1's).

The a? is equal to a![a,a, ...[a, a, aa a]... a a] (a a's)!