Visualization of tetpeno using exponentiation

The tetpeno is equal to s(4,4,5) in strong array notation.[1] The term was coined by wiki user Hyp cos. It can be represented in up-arrow notation as \(4\uparrow\uparrow\uparrow\uparrow\uparrow4\) (4 heptated to 4).

This number is also equal to s(4,2,6) and s(4,5,1,2).


The name of this number is based on the word "tetra" and "penta" (Greek for 4 and 5), meaning a base-4 number, generated using hyper-5 operation based on exponentiation.


Notation Approximation
Up-arrow notation \(4\uparrow\uparrow\uparrow\uparrow\uparrow4\) (exact)
BEAF \(\{4,4,5\}\) (exact)
Hyper-E notation \(E(4)1\#1\#1\#1\#4\) (exact)
Chained arrow notation \(4\rightarrow4\rightarrow5\) (exact)
Hyperfactorial array notation \(5!4\)
Fast-growing hierarchy \(f_6(3)\)
Hardy hierarchy \(H_{\omega^6}(3)\)
Slow-growing hierarchy \(g_{\varphi(4,0)}(4)\)


  1. Numbers from linear array notation | Steps Toward Infinity!

See alsoEdit

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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