Pentation

Pentation or quintation refers to the function \(a \uparrow\uparrow\uparrow b\), where Arrow Notation is used. It produces numbers very much larger than those produced by tetration.

Pentation can be written in Knuth's up-arrow notation as $$a \uparrow \uparrow \uparrow b$$ or $$a \uparrow^{3}b$$.

Pentation is less known than its tetrational cousin, but there are a few googologisms employing it: 3 pentated to 3 is known as the tritri, and 10 pentated to 100 is gaggol.

Sunir Shah uses the notation \(a * b\) to indicate this function. Bowers calls it 'a to the b'th tower'. Sbiis Saibian uses the notation \(_{b \leftarrow}a\).

Pseudocode
Below is an example of pseudocode for pentation.

function pentation(a, b): result := 1 repeat b times: result := a tetrated to result return result