The Ackermann numbers are a sequence defined using Arrow Notation as \[A(n) = n\underbrace{\uparrow\uparrow...\uparrow\uparrow}_nn\] where \(n\) is a positive integer. The first few Ackermann numbers are \(1\uparrow 1 = 1\), \(2\uparrow\uparrow 2 = 4\), and \(3\uparrow\uparrow\uparrow 3 =\) tritri. More generally, the Ackermann numbers diagonalize over arrow notation, and signify its growth rate is approximately \(f_\omega(n)\) in FGH and \(g_{\varphi(n-1,0)}(n)\) in SGH. The \(n\)th Ackermann number could also be written \(3\)\(\&\)\(n\) or \(\lbrace n,n,n brace\) in BEAF.