
Visualization of tettro using exponentiation
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). It is approximately 10↑↑10↑↑1010154.
This number is also equal to s(4,2,4) and s(4,3,1,2).
Etymology[]
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.
Computation[]
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 \(f(f(f(4)))\).
Approximations[]
Notation | Approximation |
---|---|
Arrow notation | \(4\uparrow\uparrow\uparrow4\) (exact) |
Bowers' Exploding Array Function | \(\{4,4,3\}\) (exact) |
Chained arrow notation | \(4\rightarrow4\rightarrow3\) (exact) |
Hyper-E notation | \(\textrm E(4)1\#1\#4\) (exact) |
Hyperfactorial array notation | \(5!2\) |
Steinhaus-Moser Notation | 4[5] |
Fast-growing hierarchy | \(f_4(3)\) |
Hardy hierarchy | \(H_{\omega^4}(3)\) |
Slow-growing hierarchy | \(g_{\zeta_0}(4)\) |
See also[]
3-entry series
4-entry series
Primitol group: primitol · primitolplex · primitolbiplex · primitoltriplex · primitolquadriplex · primibol · primibolplex · primitrol · primitrolplex · primitetol · primitetolplex · primipenol · primipenolplex
Tetentri group: duprimitol · duprimitolplex · duprimibol · tetentri
Tetentet group: truprimitol · truprimitolplex · truprimibol · truprimibolplex · tetentet
Tetenpent group: quadprimitol · quadprimitolplex · quadprimibol · quadprimibolplex · tetenpent
Tetenhex group: quinprimitol · quinprimitolplex · quinprimibol · quinprimibolplex · tetenhex
Tetentri group: duprimitol · duprimitolplex · duprimibol · tetentri
Tetentet group: truprimitol · truprimitolplex · truprimibol · truprimibolplex · tetentet
Tetenpent group: quadprimitol · quadprimitolplex · quadprimibol · quadprimibolplex · tetenpent
Tetenhex group: quinprimitol · quinprimitolplex · quinprimibol · quinprimibolplex · tetenhex
5-entry series
Chainol group: chainol · chainolplex · chainolbiplex · chainoltriplex · chainolquadriplex · chainbol · chainbolplex · chaintrol · chaintrolplex
Chainprimol group: chainprimol · chainprimolplex · chainpribol · chainpribolplex · chainduprimol · chainduprimolplex · chaindupribol · chaindupribolplex · chaintruprimol · chaintruprimolplex · chaintrupribol · chaintrupribolplex
Pententri group: duchainol · duchainolplex · duchainbol · duchainbolplex · duchainprimol · duchainprimolplex · duchainpribol · duchainpribolplex · duchainduprimol · duchainduprimolplex · duchaindupribol · pententri
Pententet group: truchainol · truchainolplex · truchainbol · truchainbolplex · truchainprimol · truchainprimolplex · truchainpribol · truchainpribolplex · truchainduprimol · truchainduprimolplex · truchaindupribol · truchaindupribolplex · pententet · pentenpent · pentenhex
Chainprimol group: chainprimol · chainprimolplex · chainpribol · chainpribolplex · chainduprimol · chainduprimolplex · chaindupribol · chaindupribolplex · chaintruprimol · chaintruprimolplex · chaintrupribol · chaintrupribolplex
Pententri group: duchainol · duchainolplex · duchainbol · duchainbolplex · duchainprimol · duchainprimolplex · duchainpribol · duchainpribolplex · duchainduprimol · duchainduprimolplex · duchaindupribol · pententri
Pententet group: truchainol · truchainolplex · truchainbol · truchainbolplex · truchainprimol · truchainprimolplex · truchainpribol · truchainpribolplex · truchainduprimol · truchainduprimolplex · truchaindupribol · truchaindupribolplex · pententet · pentenpent · pentenhex
6-entry series
Choinol group: choinol · choinolplex · choinalbiplex · choinbol · choinbolplex · choinprimol · choinprimolplex · choinpribol · choinpribolplex · choinduprimol · choinduprimolplex · choindupribol · choindupribolplex
Choichainol group: choichainol · choichainolplex · choichainbolplex · choichainpribolplex · choichaindupribolplex · choiduchaindupribolplex
Hexentri group: hexentri · hexentet · hexenpent · hexenhex
Choichainol group: choichainol · choichainolplex · choichainbolplex · choichainpribolplex · choichaindupribolplex · choiduchaindupribolplex
Hexentri group: hexentri · hexentet · hexenpent · hexenhex