Octation refers to the 8th hyperoperation starting from addition. It is equal to the binary functions \(\uparrow\uparrow\uparrow\uparrow\uparrow\uparrow\) or \(\uparrow^{6}\) in Knuth's up-arrow notation[1]
"a octated to b" can be written in array notation as \(\{a,b,6\}\), in chained arrow notation as \(a \rightarrow b \rightarrow 6\) and in Hyper-E notation as E[a]1#1#1#1#1#b.
Octational growth rate is approximately \(f_7(n)\) in the fast-growing hierarchy.
Pseudocode[]
Below is an example of pseudocode[2] for octation.
function octation(a, b):
result := 1
repeat b times:
result := a heptated to result
return result
Sources[]
See also[]
Main article: hyper operator
Hyper-operators: successor · addition · multiplication · exponentiation · tetration · pentation · hexation · heptation · octation · enneation · decation (un/doe/tre) · vigintation (doe) · trigintation · centation (tri) · docentation · myriation · circulationBowers' extensions: expansion · multiexpansion · powerexpansion · expandotetration · explosion (multi/power/tetra) · detonation · pentonation
Saibian's extensions: hexonation · heptonation · octonation · ennonation · deconation
Tiaokhiao's extensions: megotion (multi/power/tetra) · megoexpansion (multi/power/tetra) · megoexplosion · megodetonation · gigotion (expand/explod/deto) · terotion · more...