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

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.[1]

Boboris02 calls this number Hexar, which also equals $$Q_{1,0}(6)=Q_{6}(6)$$ in the Q-supersystem.[2]

## EtymologyEdit

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".

## ComputationEdit

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 $$f(f(f(f(f(6)))))$$.

## ApproximationsEdit

Notation Approximation
Up-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 $$g_{\varphi(3,0)}(6)$$