[seqfan] Some large numbers

[franktaw at netscape.net]

Consider https://oeis.org/A014221 - a(n+1) = 2^a(n), and 
https://oeis.org/A014221 - a(n+1) = 3^a(n).
Now merge the two sequences:

0, 1, 2, 3, 4, 16, 27, 65536, 7625597484987[, 2^65536]

We're interested here in how the merge proceeds, so drop the initial 0, 
1, and replace each subsequent term with it's base:

2, 3, 2, 2, 3, 2, 3[, 2]

How does this sequence continue? Does it alternate from here between 
2's and 3's, or are there more 2,2 substrings? Is there an efficient 
way to compute the sequence?

Franklin T. Adams-Watters