Latri

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Visual representation of Latri

Latri is equal to {3,3,3 (1) 2} = {3,3 (1) 3} = {3,2 (1) 4} in BEAF. The term was coined by Jonathan Bowers.

Latri is comparable to \(f_{\omega^\omega+2}(3)\) in the fast-growing hierarchy.

Computation

Latri can be computed in the following process:

1. Let a₁ = 3.
2. Let a₂ = {3,3,3} (a.k.a. tritri).
3. Let a₃ = {3,3,...,3,3} (where the number of threes is a₂) = {3,{3,3,3} (1) 2} (a.k.a. dupertri).
4. Continuing, let a_n = {3,3,...,3,3} (with a_{n - 1} threes) = {3,a_{n - 1} (1) 2}.
5. Latri is equal to a_a3.

Approximations

Notation	Approximation
Bird's array notation	\(\{3,3,3 [2] 2\}\) (exact)
Cascading-E notation	\(\textrm E3\#\text{^}\#3\#3\#3\)
Hyperfactorial array notation	\(3![3,1,1,2]\)
Fast-growing hierarchy	\(f_{\omega^{\omega}+1}(f_{\omega^{\omega}}(\text{tritri}))\) \(\approx f_{\omega^\omega+1}(f_{\omega^\omega}(f_3(f_2(35))))\)
X-Sequence Hyper-Exponential Notation	\(3\{X^X+1\}3\{X^X\}3\{3\}3\)
Hardy hierarchy	\(H_{\omega^{\omega^{\omega}+1}+\omega^{\omega^{\omega}}+\omega^{4}}(3)\)
Slow-growing hierarchy	\(g_{\theta(\Omega^\Omega,\theta(\Omega^\Omega))}(3)\)

See also

Jonathan Bowers' tritri series

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
TheInfinitySeeker's extensions: dutritritri