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Tettro

Visualization of tettro using exponentiation

The tettro is equal to s(4,4,3) in strong array notation.[1] The term was coined by Wikia user Hyp cos. It can be represented in up-arrow notation as \(4\uparrow\uparrow\uparrow4\) (4 pentated to 4).

This number is also equal to s(4,2,4) and s(4,3,1,2).

EtymologyEdit

The name of this number is based on the word "tetra" and "tri" (Greek for 4 and 3), meaning a base-4 number, generated using hyper-3 operation based on exponentiation.

ComputationEdit

Tettro can be computed in the following process:

  • \(f(1)=4\)
  • \(f(2)=4^4=256\)
  • \(f(3)=4^{4^4}\approx1.3408\times10^{154}\)
  • \(f(4)=4^{4^{4^4}}\), a.k.a. tetbo
  • etc.
  • Tettro equals \(f(f(f(4)))\).

ApproximationsEdit

Notation Approximation
Up-arrow notation \(4\uparrow\uparrow\uparrow4\) (exact)
BEAF \(\{4,4,3\}\) (exact)
Hyper-E notation \(E(4)1\#1\#4\) (exact)
Chained arrow notation \(4\rightarrow4\rightarrow3\) (exact)
Hyperfactorial array notation \(5!2\)
Fast-growing hierarchy \(f_4(3)\)
Hardy hierarchy \(H_{\omega^4}(3)\)
Slow-growing hierarchy \(g_{\zeta_0}(4)\)

See alsoEdit

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


SourcesEdit

  1. Numbers from linear array notation | Steps Toward Infinity!

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