Hextro

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Visualization of hextro using exponentiation

Hextro is equal to s(6,6,3) in strong array notation. The term was coined by wiki user Hyp cos. It can be represented in up-arrow notation as $6\uparrow \uparrow \uparrow 6$ (6 pentated to 6).

This number is also equal to s(6,2,4) and s(6,3,1,2).

Etymology

The name of this number is based on the word "hexa" and "tri" (Greek for 6 and 3), meaning a base-6 number, generated using hyper-3 operation based on exponentiation.

Computation

Hextro can be computed in the following process:

• $f(1)=6$
• $f(2)=6^{6}=46656$
• $f(3)=6^{6^{6}}\approx 2.6591\times 10^{36305}$
• $f(4)=6^{6^{6^{6}}}$
• etc.
• Hextro equals $f(f(f(f(f(6)))))$.

Approximations

Notation	Approximation
Arrow notation	$6\uparrow \uparrow \uparrow 6$ (exact)
Bowers' Exploding Array Function	$\{6,6,3\}$ (exact)
Chained arrow notation	$6\rightarrow 6\rightarrow 3$ (exact)
Hyper-E notation	${\textrm {E}}[6]1\#1\#6$ (exact), ${\textrm {E}}36305.31580191892\#4\#5$
Hyperfactorial array notation	$7!2$
Steinhaus-Moser Notation	$6[5]$
Fast-growing hierarchy	$f_{4}(5)$
Hardy hierarchy	$H_{\omega ^{4}}(5)$
Slow-growing hierarchy	$g_{\zeta _{0}}(6)$

See also

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

4-entry series

Primitol group: primitol · primitolplex · primitolbiplex · primitoltriplex · primitolquadriplex · primibol · primibolplex · primitrol · primitrolplex · primitetol · primitetolplex · primipenol · primipenolplex
Tetentri group: duprimitol · duprimitolplex · duprimibol · tetentri
Tetentet group: truprimitol · truprimitolplex · truprimibol · truprimibolplex · tetentet
Tetenpent group: quadprimitol · quadprimitolplex · quadprimibol · quadprimibolplex · tetenpent
Tetenhex group: quinprimitol · quinprimitolplex · quinprimibol · quinprimibolplex · tetenhex

5-entry series

Chainol group: chainol · chainolplex · chainolbiplex · chainoltriplex · chainolquadriplex · chainbol · chainbolplex · chaintrol · chaintrolplex
Chainprimol group: chainprimol · chainprimolplex · chainpribol · chainpribolplex · chainduprimol · chainduprimolplex · chaindupribol · chaindupribolplex · chaintruprimol · chaintruprimolplex · chaintrupribol · chaintrupribolplex
Pententri group: duchainol · duchainolplex · duchainbol · duchainbolplex · duchainprimol · duchainprimolplex · duchainpribol · duchainpribolplex · duchainduprimol · duchainduprimolplex · duchaindupribol · pententri
Pententet group: truchainol · truchainolplex · truchainbol · truchainbolplex · truchainprimol · truchainprimolplex · truchainpribol · truchainpribolplex · truchainduprimol · truchainduprimolplex · truchaindupribol · truchaindupribolplex · pententet · pentenpent · pentenhex

6-entry series

Choinol group: choinol · choinolplex · choinalbiplex · choinbol · choinbolplex · choinprimol · choinprimolplex · choinpribol · choinpribolplex · choinduprimol · choinduprimolplex · choindupribol · choindupribolplex
Choichainol group: choichainol · choichainolplex · choichainbolplex · choichainpribolplex · choichaindupribolplex · choiduchaindupribolplex
Hexentri group: hexentri · hexentet · hexenpent · hexenhex