Pentatri is equal to {3,3,3,3,3} or {3,5 (1) 2} (3 powergigoexploded to 3) in BEAF. or 5 & 3, using the array of operator. The term was coined by Jonathan Bowers.

It is also quite close to the lower bound for $$G(16)$$ in the Goodstein function, which illustrates that large numbers can appear in the modern mathematics.

Chris Bird noted that Friedman's n(k) function is comparable to {3,k (1) 2}, so pentatri should be in ballpark with n(5).

## Contents

### Etymology

The name of this number is based on the words "penta-" (greek: five) and "tri-" (greek: three), meaning that there are 5 3's in the array.

### Approximations in other notations

Notation Approximation
BEAF $$\{3,3,3,3,3\}$$ or $$\{3,5(1)2\}$$ (both equal)
Bird's array notation $$\{3,3,3,3,3\}$$ (exactly equal)
Hyper-E notation E(3)3####3
X-Sequence Hyper-Exponential Notation $$3\{X^3\}3$$
Multivariable Ackermann $$A(1,0,0,0,3)$$
Strong array notation s(3,4,4,3,3)
Fast-growing hierarchy $$f_{\omega^{3}}(3)$$
Hardy hierarchy $$H_{\omega^{\omega^{3}}}(3)$$
Slow-growing hierarchy $$g_{\varphi(2,3,3,0)}(3)$$

### Sources

1. Bowers, JonathanInfinity Scrapers. Retrieved January 2013.
2. Bird, ChrisLinear Array Notation. Retrieved 03.03.2013.

Tritri series: tritri · tritet · tripent · trisept · tridecal · grand tridecal
Tetratri series: tetratri · supertet · general(plex)
Pentatri series: pentatri · superpent · pentadecal(plex)
Hexatri series: hexatri · superhex · hexadecal(plex)
Heptatri series: heptatri · supersept · heptadecal
Iteral series: superoct · octadecal · superenn · ennadecal · iteral · ultatri
Dupertri series: dupertri · duperdecal · truperdecal · quadruperdecal
Latri series: latri · emperal(plex) · hyperal(plex) · admiral
Dutritri series: dutritri · dutridecal
Dimentri series: dimentri · dulatri · trilatri · trimentri
Triakulus series: triakulus · tridecatrix
Big boowa series: big boowa · great big boowa · grand boowa
Tiaokhiao's extensions: trihex · trioct · triennet · triundecal · tridodecal · tritriplex · tritriplexian · grand tritri · tetrapent · tetrahex · grand tetratri · octatri · enneatri · decatri · undecatri · dodecatri