Hexation or sextation refers to the 6th hyperoperation if addition is to be regarded as the first. It is equal to a↑↑↑↑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→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→b→4 and in Hyper-E notation as E(a)1#1#1#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".[4]

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 = 

3 ↑↑↑↑ 8 = 3↑↑↑3↑↑↑3↑↑↑3↑↑↑3↑↑↑3↑↑↑3↑↑↑3

Sources

See also

Community content is available under CC-BY-SA unless otherwise noted.