Powers of 2

Powers of two are often used in Googology. can be represented as  within Sbiis Saibian's ExE and   utilizing Jonathan Bowers' BEAF.

Miscellaneous
Due to the intriguing property that the log10 of 2 is equal to ~0.30103 and 1/0.30103 is so close to 3, it means that 210 = 1,024 will be approximately 103 as well. Owing to this, the first few values of  for smallish n yield numbers that gradually diverge from. In fact, when the prior 128 powers of two are stripped of all but their first digits and listed like so, one can observe the first digit of  tends to stay fixed for successive m and constant a:

2481361251 2481361251 2481361251 2481361251 2481371251 2491371251 2491371251 2491371361 2491371361 2491371361 2512481361 2512481361 25124813