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Some examples: \begin{align*} 1 &= 1^1 \\ 4 &= 2^2 \\ 27 &= 3^3 \\ 256 &= 4^4 \\ 3125 &= 5^5 \\ \end{align*} and so on. Is there a name for these types of numbers? It seems like there should be.

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    $\begingroup$ As exponentiation is repeated multiplication, tetration is a term for repeated exponentiation. The simplest case would be a number raised to itself as a power. $\endgroup$ – hardmath Feb 1 '14 at 23:55
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    $\begingroup$ Self power ? $\endgroup$ – Lucian Feb 2 '14 at 0:24

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