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Hexation or sextation refers to the 6th hyperoperation starting from addition. 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]


Here are some examples of hexation in action:

\(1 \uparrow^{4} b = 1\)

\(a \uparrow^{4} 1 = a\)

\(2 \uparrow^{4} 2 = 4\)

\(2 \uparrow^{4} 3 ={^{65536}}2\)

\(3\)\(\uparrow^{4} 2 = 3 \uparrow\uparrow\uparrow 3 = {^{7625597484987}}3\)

\(3 \uparrow^{4} 3 = 3 \uparrow\uparrow\uparrow\)\(tritri\)

\(4 \uparrow^{4} 2 = 4 \uparrow\uparrow\uparrow 4\) = \(^{^{^{4}4}4}4\)

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.

See also Edit

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