Trihex is equal to \(\lbrace6,6,6\rbrace\) or \(6\lbrace6\rbrace6\) in BEAF, \(6\uparrow\uparrow\uparrow\uparrow\uparrow\uparrow6\) in arrow notation, or 6 octated to 6.[1]. The term was coined by Aarex Tiaokhiao. This is the sixth Ackermann number.
Trihex visualized using iterated power towers.
Googology Wiki user Hyp cos calls this number a trienhex, and it's equal to s(6,6,6), s(6,2,7), s(6,6,1,2), s(6,1,1,3), or s(6,1,1,1,2) in strong array notation.[2]
Etymology[]
The name of this number is based on Greek prefixes tri- (three) and hexa- (six), meaning that there are 3 6's in the array.
Approximations[]
| Notation | Approximation |
|---|---|
| Arrow notation | \(6\uparrow\uparrow\uparrow\uparrow\uparrow\uparrow6\) (exact) |
| Bowers' Exploding Array Function | \(\{6,6,6\}\) (exact) |
| Chained arrow notation | \(6\rightarrow6\rightarrow6\) (exact) |
| Hyper-E notation | \(\textrm E[6]1\#1\#1\#1\#1\#6\) (exact) \(\approx\textrm E4.67\#1\#1\#1\#1\#6\) (base 10 approximation) |
| Hyperfactorial array notation | \(6!5\) |
| Fast-growing hierarchy | \(f_7(5)\) |
| Hardy hierarchy | \(H_{\omega^7}(5)\) |
| Slow-growing hierarchy | \(g_{\varphi(5,0)}(6)\) |
Sources[]
- ↑ Tiaokhiao, Aarex. Aarex's Array Notation. Retrieved December 2013.
- ↑ Numbers from linear array notation | Steps Toward Infinity!
See also[]
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) · diteral(plex) · admiral
Dutritri series: dutritri · dutridecal
Dimentri series: dimentri · dimendecal · 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
RedBandServerYT's extensions: tridecalplex
Douglas Shamlin Jr.'s extensions: grand tridecalplex · quintuperdecal · triteral · dutetradecal · quadriteral · dupentadecal · duladecal · triladecal
MultiArrest91's extensions: tritredecal · tritetradecal · sextuperdecal · septuperdecal · octuperdecal · nonuperdecal · decuperdecal · centuperdecal · milluperdecal · quadritetradecal · quintitridecal
SeveralLegend9998's extensions: corboral
XRQ CORPORATION's extensions: grand tridecal · grand emperal · grand grand emperal · quintiteral · quadrilatri · quintilatri · sextilatri · septilatri · octilatri · nonilatri · decilatri
Exeen Management World's extensions: dutritet · dutetratet · dupentapent · duheptasept · duheptadecal · duoctadecal · duennadecal · grand dutritri · demperal · tritridecal · tritetradecal · quadritridecal
BAT4423's extension: duhexadecal
ARsygo's extensions: tritridex · tritetdex · grand tritet · grand tripent · grand dozenal · grand trihectal · grand tritriplex · great tridecal · gigantic tridecal · gorged tridecal · gulp tridecal · gasp tridecal · tetrahept · tetraoct · tetraenn · grand tetradecal · pentatet · hexatet · hexapent