
Tripent visualized using iterated power towers.

"Fashion" view of tripent using iterated power towers with arrows.
Tripent is equal to \(\lbrace5,5,5\rbrace\) or \(5\lbrace5\rbrace5\) in BEAF, \(5\uparrow\uparrow\uparrow\uparrow\uparrow5\) in arrow notation, or 5 heptated to 5.[1]. The term was coined by Jonathan Bowers. This is the fifth Ackermann number.
Googology Wiki user Hyp cos calls this number a trienpent, and it's equal to s(5,5,5), s(5,2,6), s(5,5,1,2), s(5,1,1,3), or s(5,1,1,1,2) in strong array notation. [2]
It can be computed during the following process:
- \(A(1)\) = 5
- \(A(2)\) = 5^5^5^5^5 (A(1) 5's)
- \(A(3)\) = 5^5^5^...5^5^5, with A(2) 5's.
- \(A(4)\) = 5^5^5^5^5^......5^5^5^5, with A(3) 5's
- Continue, let \(A(n)\) be 5^5^5^5^......^5^5^5 with \(A(n-1)\) 5's
- Tripent is . \(A^{A^{A^{A^{5}(1)}(1)}(1)}(1)\)
Etymology[]
The name of this number is based on tri- (three) and penta- (five), meaning that there are 3 5's in the array.
Approximations[]
Notation | Approximation |
---|---|
Arrow notation | \(5\uparrow\uparrow\uparrow\uparrow\uparrow5\) (exact) |
Bowers' Exploding Array Function | \(\{5,5,5\}\) (exact) |
Chained arrow notation | \(5\rightarrow5\rightarrow5\) (exact) |
Hyper-E notation | \(\textrm E[5]1\#1\#1\#1\#5\) (exact) |
Hyperfactorial array notation | \(6!4\) |
Steinhaus-Moser Notation | \(4[6][6][6][6]\) |
Fast-growing hierarchy | \(f_6(4)\) |
Hardy hierarchy | \(H_{\omega^6}(4)\) |
Slow-growing hierarchy | \(g_{\varphi(4,0)}(5)\) |
Sources[]
- ↑ Bowers, Jonathan. Infinity Scrapers. Retrieved January 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