User blog comment:Flavio61/Louis Epstein number list/@comment-27173506-20160118190252/@comment-5529393-20160208230744

a u b is between a ^^ b and a ^^ (2^b).

3 u 4 < 3 ^^ 16

3 uu 4 < 3 u (3 ^^ 16) < 3 ^^ (2^(3^^16))

3 uuu 4 < 3 u 3^^(3^^17) < 3 ^^ (3^^(2^(3^^16)+1))

3 uuuu 4 < 3 u 3 ^^ (3^^(2^(3^^16)+1)) < 3 ^^ (3 ^^ (3 ^^ (2^(3^^16)+1)+1)) < 3^^3^^3^^3^^17 < 3^^^6, which is certainly much less than 4^^^^3.