^{57}). I thought perhaps the use of successive exponentiation in the form n

_{1}^n

_{2}^n

_{3}^n

_{4}might be a possibility with very low information density.

I used Excel to autogenerate all possible combinations of n

_{1}^n

_{2}^n

_{3}^n

_{4}, using n = 2..9, and found that I could form the following values which were within an order of magnitude of 10

^{57}:

- 4.1359e56
- 7.8464e56
- 1.7970e57
- 6.2771e57
- 2.2980e58

I wanted more precision, though, so I added another exponent slot and repeated the process using the form n

_{1}^n

_{2}^n

_{3}^n

_{4}^n

_{5}.

To my chagrin, although I found many more combinations that yielded the above values, I didn't find any new values in between them. It would seem, then, that for any maximum value n

_{max}, there is only a very limited number of values which can be formed as the result of n

_{1}^n

_{2}^..., where n is a whole number, and this holds regardless of how many n-values you use.

Is this something that's already well-known and has an obvious name? Like, "Oh, right, the Pulling-Dolbrach numbers are those numbers which can be formed as a result of successively exponentiating whole numbers."