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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]

## Computation Edit

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 $$a_{a_3} = a_{\text{Tritri}}$$.

## ApproximationsEdit

Notation Approximation
Up-arrow notation $$3\uparrow\uparrow\uparrow\uparrow3$$ or $$3\uparrow\uparrow\uparrow\uparrow\uparrow2$$ (both exact)
BEAF $$\{3,3,4\}$$ or $$\{3,2,5\}$$ (both exact)
Hyper-E notation $$E(3)1\#1\#1\#3$$ (exact)
Chained arrow notation $$3\rightarrow3\rightarrow4$$ or $$3\rightarrow2\rightarrow5$$ (both exact)
Hyperfactorial array notation $$4!3$$
Fast-growing hierarchy $$f_5(2)$$
Hardy hierarchy $$H_{\omega^5}(2)$$
Slow-growing hierarchy $$g_{\eta_0} (3)$$

## Sources Edit

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