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"Triteto" redirects here. It is not to be confused with tritet.

The grahal is equal to $$g_1$$ in Graham's function. The term was coined by Aarex Tiaokhiao.[1]

It is equal to $$3 \uparrow\uparrow\uparrow\uparrow 3 = 3 \uparrow\uparrow\uparrow\uparrow\uparrow 2$$ in up-arrow notation.

Wiki user Hyp cos calls this number triteto, and it's equal to s(3,3,4), s(3,2,5), or s(3,4,1,2) in strong array notation. [2]

Tim Urban calls this number "NO I CAN'T EVEN" in his Wait Buy Why article "From 1,000,000 to Graham's Number".[3]

## Computation

Grahal can be computed in the following process:

• $$a_1 = 3$$
• $$a_2 = 3^{3^3} =$$ $$7,625,597,484,987$$
• $$a_3 = 3^{3^{3^{.^{.^{.^{3^3}}}}}}$$ with $$a_2$$ threes = Tritri
• $$a_4 = 3^{3^{3^{.^{.^{.^{3^3}}}}}}$$ with $$a_3$$ threes
• etc.
• Grahal is equal to $$a_{a_3} = a_{\text{Tritri}}$$.

## Approximations

Notation Approximation
Arrow notation $$3\uparrow\uparrow\uparrow\uparrow3$$ (exact)
$$=3\uparrow\uparrow\uparrow\uparrow\uparrow2$$
BEAF $$\{3,3,4\}$$ (exact)
$$=\{3,2,5\}$$
Hyper-E notation $$\textrm E[3]1\#1\#1\#3$$ (exact)
Chained arrow notation $$3\rightarrow3\rightarrow4$$ (exact)
$$3\rightarrow2\rightarrow5$$
Hyperfactorial array notation $$4!3$$
Fast-growing hierarchy $$f_4(f_3(f_2(37)))$$
Hardy hierarchy $$H_{\omega^4+\omega^3+\omega^2}(37)$$
Slow-growing hierarchy $$g_{\eta_0} (3)$$