User blog comment:Ikosarakt1/Examples for Bird's array notation/@comment-6768393-20130716233130/@comment-5150073-20130717082738

I can do better: we can note that {3,5,1,1,2} requires 4 repeations of "of length" in your expression. Since adding 1 to the argument of function f(n) = {3,n,1,1,2} adds one such repeation, we can say, that, in general: {3,n,1,1,2} requires n-1 of them.

The number {3,3,2,1,2} = {3,{3,2,2,1,2},1,1,2} = {3,{3,3,1,1,2},1,1,2} would require {3,3,1,1,2}-1 repeations of "of length", and in general:

{3,n,2,1,2} requires {3,n-1,2,1,2}-1 repeations of "of length" to express comparable number in CAN.

We can imagine that already number {3,3,3,1,2} = {3,{3,2,3,1,2},2,1,2} = {3,{3,3,2,1,2},2,1,2}

actually surpasses even this system.

However, that's only goes for the original CAN, if we allow to use Peter Hurford's extensions, then I believe that pentatri = {3,3,3,3,3} is comparable (in googologists' sense, of course) to

the number 3 →4 3.