User blog:Nayuta Ito/Guessing the definition of PGN from Psi's Current Value Of PEGG

When I update the PEGG detailed log, I check Psi's blog "Current Value Of PEGG" to ensure my values. However, there is something labeled PGN (Psi's Geometric Notation) in the approximation. Since I (and some other people) couldn't find the original definition, so I will guess the definition in this blog.

From many days of observation, I guess:

$$[a_n,a_{n-1},...,a_2,a_1;n]=(10\uparrow^n)^{a_n}(10\uparrow^{n-1})^{a_{n-1}}\cdots(10\uparrow\uparrow)^{a_2}(10\uparrow)^{a_1}n $$

Even though this works as a definition, but I will write it in a recursive form:

A is comma-separated array.

$$[0,A;n]=[A;n]$$

$$[0;n]=n$$

$$[A,a+1;n]=[A,a;10^n]$$

$$[a,0,C;n]=[n-1,C;10]$$, where C is 0 or more zeros.

I guess I need only these to work... Please tell me If I did something wrong.