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. Jonathan Bowers calls it 'a to the b'th layer'. Sbiis Saibian proposes the notation a→b in analogy to ba for tetration, but he usually uses up-arrows.
Hexational growth rate is approximately \(f_5(n)\) in the fast-growing hierarchy.
Tim Urban calls hexation a "power tower feeding frenzy psycho festival".
Here are some examples of hexational-level calculations.
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