User blog comment:Flavio61/Louis Epstein number list/@comment-27173506-20160118190252/@comment-12.144.5.30-20160119184906

OK,so you are looking for a Knuth style expansion (3^^^3=3^^3^^3).

I use 3 uuu 3 = 3 uu (3 u 3) = 3 u (3 u (3 u 3)).

Nesting on the bound is superior to nesting on the base...3 ((3 u 3) u 3)u) 3 < 3 ((3 u (3 u 3) u) 3.

3 uuu 3 let alone the others far exceeds 3^^^3.