What is the name for this: "x^^y" (as in 2^^2=2^2 and 3^^3=3^3^3 and so on)

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How do you call / is there any specific name for the following:

x^^y

e.g.:

  • 2^^2 = 2^2
  • 3^^3 = 3^3^3
  • 4^^4 = 4^4^4^4
  • ...
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This is known as tetration, where $^na$ is $a^{a^{a^{...}}}$ with $n$ copies of $a$ in the exponentiation. You might also seen it written as $a \uparrow \uparrow n$.

To learn more about these kinds of compound arithmetic operators, I recommend reading about Knuth's up-arrow notation.