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Not to be confused with tripent.

Visualization of tripeno using exponentiation

Tripeno is equal to s(3,3,5) in strong array notation.[1] The term was coined by wiki user Hyp cos. It can be represented in up-arrow notation as \(3\uparrow\uparrow\uparrow\uparrow\uparrow3\) (3 heptated to 3).

This number is also equal to s(3,2,6) and s(3,5,1,2).

Aarex Tiaokhiao calls this number biahal.[2]

Etymology

The name of this number is based on the word "tri" and "penta" (Greek for 3 and 5), meaning a base-3 number, generated using hyper-5 operation based on exponentiation.

Approximations

Notation Approximation
Arrow notation \(3\uparrow\uparrow\uparrow\uparrow\uparrow3\) (exact)
BEAF \(\{3,3,5\}\) (exact)
Hyper-E notation \(\textrm E[3]1\#1\#1\#1\#3\) (exact)
Chained arrow notation \(3\rightarrow3\rightarrow5\) (exact)
Hyperfactorial array notation \(4!4\)
Fast-growing hierarchy \(f_6(2)\)
Hardy hierarchy \(H_{\omega^6}(2)\)
Slow-growing hierarchy \(g_{\varphi(4,0)}(3)\)

Sources

  1. Numbers from linear array notation | Steps Toward Infinity!
  2. Tiaokhiao, Aarex. Forcal - Aarex's Large Numbers. Retrieved 2021-05-30. (original link is dead)

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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