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5-triteto

Visualization of grahal using exponentiation

The grahal is equal to G(1) in Graham's function. The term was coined by Aarex Tiaokhiao.[1]

It is equal to \(3 \uparrow\uparrow\uparrow\uparrow 3 = 3 \uparrow\uparrow\uparrow\uparrow\uparrow 2\) in up-arrow notation.

Wiki user Hyp cos calls this number triteto, and it's equal to s(3,3,4), s(3,2,5), or s(3,4,1,2) in strong array notation. [2]

Computation Edit

Grahal can be computed in the following process:

  • \(a_1 = 3\)
  • \(a_2 = 3^{3^3} =\) \(7625597484987\)
  • \(a_3 = 3^{3^{3^{.^{.^{.^{3^3}}}}}}\) with \(a_2\) threes = Tritri
  • \(a_4 = 3^{3^{3^{.^{.^{.^{3^3}}}}}}\) with \(a_3\) threes
  • etc.
  • Grahal is equal to \(a_{a_3}\).

ApproximationsEdit

Notation Approximation
Up-arrow notation \(3\uparrow\uparrow\uparrow\uparrow3\) (exact)
BEAF \(\{3,3,4\}\) (exact)
Hyper-E notation \(E(3)1\#1\#1\#3\) (exact)
Chained arrow notation \(3\rightarrow3\rightarrow4\) (exact)
Hyperfactorial array notation \(4!3\)
Fast-growing hierarchy \(f_5(2)\)
Hardy hierarchy \(H_{\omega^5}(2)\)
Slow-growing hierarchy \(g_{\varphi(3,0)}(3)\)

Sources Edit

  1. Forcal - Aarex large numbers
  2. Numbers from linear array notation | Steps Toward Infinity!

See also Edit

Grahal group: grahal · graham grahal
Forcal group: forcal · graham forcal · graham graham forcal · graham graham graham forcal · force forcal · force force forcal · force force force forcal
Suporcal group: suporcal · force suporcal · force force suporcal · force force force suporcal · superior suporcal · superior superior suporcal · superior superior superior suporcal
Megocal group: megocal · force megocal · superior megocal · superior superior megocal · megaior megocal · megaior megaior megocal · Megaior megaior megaior megocal
Hypercal group: hypercal · force hypercal · superior hypercal · megaior hypercal · hyperior hypercal · hyperior hyperior hypercal · hyperior hyperior hyperior hypercal
Gorgcal group: gorgcal · force gorgcal · superior gorgcal · megaior gorgcal · hyperior gorgcal · gorgcaior gorgcal · gorgcaior gorgcaior gorgcal · gorgcaior gorgcaior gorgcaior gorgcal
Gulfcal group: gulfcal · gulfcaior gulfcal · gulfcaior gulfcaior gulfcal · gulfcaior gulfcaior gulfcaior gulfcal · gaspocal · gaspocaior gaspocal · gaspocaior gaspocaior gaspocal · gaspocaior gaspocaior gaspocaior gaspocal · ginorcal · ginorcaior ginorcal · ginorcaior ginorcaior ginorcal · ginorcaior ginorcaior ginorcaior ginorcal
Terribocal group: terribocal · Terribocaior Terribocal · terribuporcal · Terribuperior Terribuporcal · terribegocal · terribypercal · terriborgecal · terribulfcal · terribaspcal · terribinorcal
Tribocal group: tribocal · Tribocaior Tribocal · tribuporcal · tribegocal · tribypercal · tetribocal · tetribuporcal · pentibocal · hexibocal · heptibocal · octibocal
Tris-Terribocal group: Tris-Terribocal · Tris-Terribocaior Tris-Terribocal · Tris-Terribuporcal · Tris-Terribegorcal · Tris-Terribypercal · Tris-Terrible-Terribocal · Tris-Terrible-Tribocal · Tris-Terrible-Tetribocal · Tris-Tribocal · Tris-Tribocaior Tris-Tribocal · Tris-Trible-Terribocal · Tris-Trible-Tribocal · Tris-Trible-Tetribocal · Tris-Tetribocal · Tris-Pentibocal · Tris-Hexibocal
Teris-Terribocal group: Teris-Terribocal · Teris-Terribuporcal · Teris-Terribegorcal · Teris-Terrible-Terribocal · Teris-Terrible-Tribocal · Teris-Terrible-Tetribocal · Teris-Terrible-Tris-Terribocal · Teris-Terrible-Tris-Tribocal · Teris-Terrible-Tris-Tetribocal · Teris-Tribocal · Teris-Tetribocal · Teris-Pentibocal
Petris-Terribocal group: Petris-Terribocal · Petris-Tribocal · Petris-Tetribocal · Ectris-Terribocal · Ectris-Tribocal · Ectris-Tetribocal · Zetris-Terribocal · Zetris-Tribocal · Zetris-Tetribocal · Yotris-Terribocal · Yotris-Tribocal · Yotris-Tetribocal
Superis-Terribocal group: Superis-Terribocal · Superis-Terribuporcal · Superis-Terribmegocal · Superis-Terribypercal

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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