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Penhexo is equal to s(5,5,6) in strong array notation. [1] The term was coined by wiki user Hyp cos. It can be represented in up-arrow notation as \(5\uparrow\uparrow\uparrow\uparrow\uparrow\uparrow5\) (5 octated to 5).

This number is also equal to s(5,2,7) and s(5,6,1,2).

Etymology

The name of this number is based on the word "penta" and "hexa" (Greek for 5 and 6), meaning a base-5 number, generated using hyper-6 operation based on exponentiation.

Approximations

Notation Approximation
Arrow notation \(5\uparrow\uparrow\uparrow\uparrow\uparrow\uparrow5\) (exact)
BEAF \(\{5,5,6\}\) (exact)
Hyper-E notation \(\textrm E[5]1\#1\#1\#1\#1\#5\) (exact)
Chained arrow notation \(5\rightarrow5\rightarrow6\) (exact)
Hyperfactorial array notation \(6!5\)
Fast-growing hierarchy \(f_7(4)\)
Hardy hierarchy \(H_{\omega^7}(4)\)
Slow-growing hierarchy \(g_{\varphi(5,0)}(5)\)

Sources

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

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