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Powerexplosion refers to the binary function $$a \{\{\{3\}\}\} b = \{a,b,3,3\} = \underbrace{a \{\{\{2\}\}\} a \{\{\{2\}\}\} \ldots \{\{\{2\}\}\} a \{\{\{2\}\}\} a}_{\text{b a's}}$$, using BEAF.[1]

In the fast-growing hierarchy, $$f_{\omega2+3}(n)$$ approximately corresponds to powerexplodal growth rate.