11,328
pages

Boogasix is equal to $$6\uparrow\uparrow\uparrow\uparrow6$$, or six hexated to 6.[1]

Googology Wiki user Hyp cos call this number hexteto, and it's equal to s(6,6,4) = s(6,2,5) = s(6,4,1,2) in strong array notation.[2]

Boboris02 calls this number Hexar, which also equals $$Q_{1,0}(6)=Q_{6}(6)$$ in the Q-supersystem.[3]

## Etymology

The name "boogasix" is formed by applying the booga- prefix to 6.

The name "hexteto" is based on the word "hexa" and "tetra" (Greek for 6 and 4), meaning a base-6 number, generated using hyper-4 operation based on exponentiation.

The name "Hexar" comes from the greek word "hexa" meaning six and the suffix "-ar".

## Computation

Boogasix can be computed in the following process:

• $$f(1)=6$$
• $$f(2)=6^{6^{6^{6^{6^6}}}}$$ with f(1) 6's, a.k.a. megafugasix
• $$f(3)=6^{6^{\vdots^{6^6}}}$$ with f(2) 6's
• $$f(4)=6^{6^{\vdots^{6^6}}}$$ with f(3) 6's
• etc.
• Boogasix equals $$f(f(f(f(f(6)))))$$.

## Approximations

Notation Approximation
Arrow notation $$6\uparrow\uparrow\uparrow\uparrow6$$ (exact)
BEAF $$\{6,6,4\}$$ (exact)
Hyper-E notation $$E(6)1\#1\#1\#6$$ (exact)
Chained arrow notation $$6\rightarrow6\rightarrow4$$ (exact)
Hyperfactorial array notation $$7!3$$
Fast-growing hierarchy $$f_5(5)$$
Hardy hierarchy $$H_{\omega^5}(5)$$
Slow-growing hierarchy $$g_{\varphi(3,0)}(6)$$

## Sources

Gar-: garone · gartwo · garthree · garfour · garfive · garsix · garseven · gareight · garnine · garten · garhundred · gargoogol · gartrialogue · gargoogolplex · gargiggol
Fz-: fzone · fztwo · fzthree · fzfour · fzfive · fzsix · fzseven · fzeight · fznine · fzten · fztwenty · fzhundred · fzthousand · fzmillion · fzgoogol · fzmilliplexion · fzgoogolplex · fzgargoogolplex · fzgargantugoogolplex · fzgiggol
Fuga-: fugaone · fugatwo · fugathree · fugafour · fugafive · fugasix · fugaseven · fugaeight · fuganine · fugaten · fugaeleven · fugahundred · fugagoogol · fugagoogolplex · fugagargoogolplex · fugagargantugoogolplex · fugagiggol
Megafuga-: megafugaone · megafugatwo · megafugathree · megafugafour · megafugafive · megafugasix · megafugaseven · megafugaeight · megafuganine · megafugaten · megafugaeleven · megafugatwelve · megafugathirteen · megafugafourteen · megafugafifteen · megafugasixteen · megafugaseventeen · megafugaeighteen · megafuganineteen · megafugatwenty · megafugathirty · megafugaforty · megafugafifty · megafugasixty · megafugaseventy · megafugaeighty · megafuganinety · megafugahundred · megafugagoogol · megafugagoogolplex · megafugagargoogolplex · megafugagargantugoogolplex
Booga-: boogaone · boogatwo · boogathree · boogafour · boogafive · boogasix · boogaten boogahundred · boogagoogol · boogagoogolplex
Gag: gagone · gagtwo · gagthree · gagfour · gagfive · gagsix · gagseven · gageight · gagnine · gagten · gaggoogol · gaggoogolplex

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