Editing Knuth's up-arrow notation (section)

===Computing 2↑<sup>''n''</sup>&nbsp;''b''===

Computing <math>2\uparrow^n b</math> can be restated in terms of an infinite table. We place the numbers <math>2^b</math> in the top row, and fill the left column with values 2. To determine a number in the table, take the number immediately to the left, then look up the required number in the previous row, at the position given by the number just taken.

{| class="wikitable"
|+ Values of <math>2\uparrow^n b = {} </math> [[Hyperoperation#Notations|<math>H_{n+2}(2,b) = {} </math> <math>2[n+2]b = {} </math>]] [[Conway chained arrow notation|2 → b → n]]
|-
! {{diagonal split header|''ⁿ''|''b''}}
! 1
! 2
! 3
! 4
! 5
! 6
! formula
|-
! 1
| 2 || 4 || 8 || 16 || 32 || 64 || <math>2^b</math>
|-
! 2
| 2 || 4 || 16 || 65,536 || 2,003,...,156,736 || 212,003,...,428,736 || <math>2\uparrow\uparrow b</math>
|-
! 3
| 2 || 4 || 65,536 || 24,636,...,948,736 || 1,300,...,948,736 || 320,146,...,948,736 || <math>2\uparrow\uparrow\uparrow b</math> 
|-
! 4
| 2 || 4 || 24,636,...,948,736 || 68,225,...,948,736 || 167,167,...,948,736 || 3,449,...,948,736 || <math>2\uparrow\uparrow\uparrow\uparrow b</math>
|}

The table is the same as [[Ackermann function#Table of values|that of the Ackermann function]], except for a shift in <math>n</math> and <math>b</math>, and an addition of 3 to all values.