Fz-

Fz- is a prefix used on a number n to indicate \(n^n\) or equivalently \({^2}n\) (i.e n tetrated to 2). It was invented by Allstair Cockburn for the sole purpose for continuing the gar- prefix invented by his son as mentioned in his A Fuga Really Big Numbers blog, noting that the expression "n ns" can be found out as the square of n by children as early as before junior high.
It is equivalent to putting a number inside a triangle in Steinhaus-Moser_Notation, and \(10^{n \log n}\) as an exponential expression. It is therefore faster-growing than the most common definition of the -plex suffix, which means to take this number and output ten to the power of this number, but still within singly exponential growth.
The first few values of fz-n are 1, 4, 27, 256, 3125, 46,656, 823,543, 16,777,216, 387,420,489, and 10,000,000,000.
The fz-n sequence is used by the game "Cookie Clicker" for the price of various upgrades in the Santa minigame.
==Properties==
*Since Fz-n is repeated multiplication of n, Fz-n is divisible by n.
== In googological notations ==
Notation 	Expression
Fast-growing hierarchy 	In between \(f_2(n)\) and \(f_3(n)\)
Hardy hierarchy 	> \(H_{\omega^2}(n)\)
Slow-growing hierarchy 	\(g_{\omega^\omega}(n)\)
Steinhaus-Moser Notation	Exactly \(n[3]\) (triangle(n))
== Sources ==
== See also ==
Category:Fuga- family
Category:Numbers discussed by Alistair Cockburn
 
Category:Prefixes
Category:Functions
Category:Exponential growth rate
Category:Perfect powers