Hexation

Hexation or sextation refers to the 6th hyperoperation if addition is to be regarded as the first. It is equal to the binary function \(\uparrow\uparrow\uparrow\uparrow \) in Knuth's up-arrow notation.3.2.3 - Ascending With Up Arrows
"a hexated to b" 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. Sunir Shah uses the notation a**b to indicate this. Jonathan Bowers calls it 'a to the b'th layer'. Reuben Goodstein mentions that \(a_{b}\) would stand for pentation, analogous to how \(^{b}a\) would stand for tetration, as well as commenting that such superscripts/subscripts cannot be used for higher hyperoperators; similarly Sbiis Saibian proposes the notation a→b in analogy to ba for tetration, but he usually uses up-arrows.
In hyperlicious function, it is equal to \(h_6(a,b)\).
Hexational growth rate is approximately \(f_5(n)\) in the fast-growing hierarchy.
Tim Urban calls hexation a "power tower feeding frenzy psycho festival".From 1,000,000 to Graham’s Number. Wait But Why.
== Examples ==
Here are some examples of hexational-level calculations.
1↑↑↑↑b=1
a↑↑↑↑1=a
2↑↑↑↑2=4
2↑↑↑↑3 =2↑↑65,536 (a power tower of 2's 65,536 terms high)
3↑↑↑↑2 = 3↑↑↑3 = 3↑↑7,625,597,484,987 = tritri (a power tower of 3's 7,625,597,484,987 terms high)
3↑↑↑↑3 = 3↑↑↑tritri = g1 = grahal
4↑↑↑↑2 = 4↑↑↑4 = \(^{^{^{4}4}4}\! 4\) where \({^b} a\) denotes tetration
3 ↑↑↑↑ 8 = 3↑↑↑3↑↑↑3↑↑↑3↑↑↑3↑↑↑3↑↑↑3↑↑↑3
==Appearance in other googolisms==
Hexation is used in \(G_1\), the first value of the Graham function, which is equal to 3 hexated to 3. This number is also known as grahal.
== Pseudocode ==
Below is an example of pseudocode for hexation.
function hexation(a, b):
 result := 1
 repeat b times:
 result := a pentated to result
 return result
== Sources ==
== See also ==
* Tritri
ja:ヘキセーション
Category:Functions
Category:Binary operators
Category:BEAF
Category:Hyper operators