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Hexation or sextation refers to the 6th hyperoperation if addition is to be regarded as the first. It is equal to $$a \uparrow\uparrow\uparrow\uparrow b$$ in Knuth's up-arrow notation. Sunir Shah uses the notation $$a **\ b$$ to indicate this.[1] Jonathan Bowers calls it 'a to the b'th layer'.[2] Sbiis Saibian proposes the notation $$a_{\rightarrow b}$$ in analogy to ba for tetration, but he usually uses up-arrows.[3]

Hexation can be written in array notation as $$\{a,b,4\}$$, in chained arrow notation as $$a \rightarrow b \rightarrow 4$$ and in Hyper-E notation as E(a)1#1#1#b.

Hexational growth rate is equivalent to $$f_5(n)$$ in the fast-growing hierarchy.

Tim Urban calls hexation a "power tower feeding frenzy psycho festival".[4]

## Examples Edit

Here are some examples of hexational-level calculations.

$$1 \uparrow^{4} b = 1$$

$$a \uparrow^{4} 1 = a$$

$$2 \uparrow^{4} 2 = 4$$

$$2 \uparrow^{4} 3 ={^{65,536}}2$$

$$3 \uparrow^{4} 2 = 3 \uparrow\uparrow\uparrow 3 = {^{7,625,597,484,987}}3$$

$$3 \uparrow^{4} 3 = 3 \uparrow\uparrow\uparrow \text{tritri} = g_{1}$$

$$4 \uparrow^{4} 2 = 4 \uparrow\uparrow\uparrow 4$$ = $$^{^{^{4}4}4}4$$

## Sources Edit

1. [1]
2. [2]
3. 3.2.3 - Ascending With Up Arrows
4. From 1,000,000 to Graham’s Number. Wait But Why.