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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 to continue the gar- prefix invented by his son.[1]

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 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 $$f_2(n)$$$${^*<}$$$$\text{fz}-n{^*<}f_3(n)$$
Hardy hierarchy greater than $$H_{\omega^2}(n)$$
Slow-growing hierarchy $$g_{\omega^\omega}(n)$$
Steinhaus-Moser Notation $$n[3]$$ (triangle(n)) (exact)