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Tetration related to iterated exponentiation


 ^2n = n^n

^3n = {(^2n)}^{(n^{n-1})}

^4n = {(^3n)}^{(n^{(^2n-n}))}

^5n = {(^4n)}^{(n^{(^3n-^2n}))}

^6n = {(^5n)}^{(n^{(^4n-^3n}))}

^kn = {(^{(k-1)}n)}^{(n^{(^{(k-2)}n-^{(k-3)}n}))} Only for K > 3


With enough nesting you can express tetration with only n and exponentiation by replacing the corresponding equalities. For example:  ^4n =  {({(n^n)}^{(n^{n-1})})}^{(n^{(n^n-n)})}

Can this be noteworthy enough to be added in the tetration page?

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