HP Prime and TI-84 Plus CE: Tetration, Iterated Exponentiation
Tetration is iterated exponentiation. A common notation of tetration is the use of two upward arrows, known as Knuth’s up-arrow notation. In general:
‘x ↑ ↑ y = x ^ x ^ x ^ … ^ x (y times)
Take the x to its own power y times.
2 ↑ ↑ 2 = 2 ^ 2 ^ 2 = 2 ^ 4 = 16
3 ↑ ↑ 2 = 3 ^ 3 ^ 3 = 3 ^ 27 = 7625597484987
4 ↑ ↑ 2 = 4 ^ 4 ^ 4 = 4 ^ 256 =
≈ 1.34078078079299 * 10^154
First, thank goodness that the HP Prime can handle really long integers in CAS mode. Second, you can quickly see how fast the results grow in tetration calculations.
In order to allow for a larger set of calculations, the programs are provided, where we break down the mantissa and exponents of each result.
HP Prime Program TETRATION
// 2018-08-14 EWS
// X^^Y, Y is an integer
FOR I FROM 1 TO Y DO
TI-84 Plus CE Program TETRATION
Disp "TETRATION X^^Y","Y: INTEGER"
“Knuth’s Up-Arrow Notation” Wikipedia. Last edited August 9, 2018. Retrieved August 14, 2018. https://en.wikipedia.org/wiki/Knuth%27s_up-arrow_notation
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