Garambois, I noticed that for all bases 2 < b < 15 you included all exponents up through and including one final exponent with a size of > 120 digits.

Would it make sense to do the same for bases 21 and 28?

The final exponent that you have shown for those bases only makes a sequence of size 119 digits. If you agree, then 21^91 and 28^83 would need to be added.

To make it easy, I quickly searched both sequences. Results are as follows:

21^91 is trivial and fairly quickly terminated.

28^83 hit a hard C113 after 6 iterations so I stopped there.

Perhaps LaurV would like to add 28^83 to his reservation since he has the base reserved.