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Gag (often used as a prefix) or Knackered Man is a function defined as $$\mathrm{gag}(n) = A(n,n)$$, where $$A(x,y)$$ stands for the Ackermann function.[1] Due to Ackermann function's relation with Arrow notation , $$\text{Gag-x} = 2\uparrow^{x-2}(x+3)-3$$

### Approximations

Notation Approximation
Arrow notation $$2\uparrow^{x-2}(x+3)-3\ BEAF \(\{2,(n-2),(n+3)\}$$
Bird's array notation $$\{2,(n-2),(n+3)\}$$
Fast-growing hierarchy $$f_\omega(n)$$