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Tettro is equal to s(4,4,3) in strong array notation.[1] The term was coined by Wikia user Hyp cos. It can be represented in up-arrow notation as $$4\uparrow\uparrow\uparrow4$$ (4 pentated to 4). It is approximately 10↑↑10↑↑1010154.

This number is also equal to s(4,2,4) and s(4,3,1,2).

## Etymology

The name of this number is based on the word "tetra" and "tri" (Greek for 4 and 3), meaning a base-4 number, generated using hyper-3 operation based on exponentiation.

## Computation

Tettro can be computed in the following process:

• $$f(1)=4$$
• $$f(2)=4^4=256$$
• $$f(3)=4^{4^4}\approx1.3408\times10^{154}$$
• $$f(4)=4^{4^{4^4}}$$, a.k.a. tetbo
• etc.
• Tettro equals $$f(f(f(4)))$$.

## Approximations

Notation Approximation
Arrow notation $$4\uparrow\uparrow\uparrow4$$ (exact)
BEAF $$\{4,4,3\}$$ (exact)
Steinhaus-Moser Notation 4[5]
Hyper-E notation $$\textrm E(4)1\#1\#4$$ (exact)
Chained arrow notation $$4\rightarrow4\rightarrow3$$ (exact)
Hyperfactorial array notation $$5!2$$
Fast-growing hierarchy $$f_4(3)$$
Hardy hierarchy $$H_{\omega^4}(3)$$
Slow-growing hierarchy $$g_{\zeta_0}(4)$$

Hyp cos' linear strong array notation numbers | exAN numbers
3-entry series
Tribo group: tribo · tetbo · pentbo · hexabo
Trientri group: trientri · tettro · pentro · hextro
Trientet group: triteto · trientet · penteto · hexteto
Trienpent group: tripeno · tetpeno · trienpent · hexpeno
Trienhex group: trihexo · tethexo · penhexo · trienhex
5-entry series
6-entry series