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For lack of better terminology (and/ or good naming skills), I'm calling this the Skyo function. It is defined as: "The Skyo of x is equal to 10 to the power of n, where n is an x amount of ones." Since this definition may be written poorly here it is in equation format: $Skyo(n)=Skyo(n-1)*10^{10^{n-1}}$

Multiple Skyos

For the case of something like $Skyo(Skyo(7))$, you would write $Skyo_{2}(7)$

For the case of $Skyo_{2}(Skyo_{2}(7))$, you would write$Skyo_{4}(7)$

List

$Skyo(0)=\text{null}$
$Skyo(1)=\text{null}*10^{10^{0}}=10$
$Skyo(2)=Skyo(1)*10^{10^{1}}=10^{11}$
$Skyo(3)=Skyo(2)*10^{10^{2}}=10^{111}$
$Skyo_{2}(1)=Skyo(Skyo(0))*10^{10^{Skyo(Skyo(0))}}=\text{null}$
$Skyo_{2}(2)=Skyo(Skyo(1))*10^{10^{Skyo(Skyo(1))}}=^{5}10$

Skyoplex

$Skyo_{10^{100}}(10^{100})=\text{Skyoplex}$
This is equal to $Skyo_{10^{100}-1}(10^{\frac{10^{100}}{9}+10^{100}-1})$