HP Prime and TI-84
Plus CE: Tetration, Iterated Exponentiation
Introduction
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.
For example:
2 ↑ ↑ 2 = 2 ^ 2 ^ 2 = 2 ^ 4 = 16
3 ↑ ↑ 2 = 3 ^ 3 ^ 3 = 3 ^ 27 = 7625597484987
4 ↑ ↑ 2 = 4 ^ 4 ^ 4 = 4 ^
256 =
13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096
≈ 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
EXPORT
TETRATION(X,Y)
BEGIN
// 2018-08-14 EWS
LOCAL I,M,E,S;
// X^^Y, Y is an integer
M:=MANT(X);
E:=XPON(X);
FOR I FROM 1 TO Y DO
S:=M*ALOG(E)*LOG(X);
M:=ALOG(FP(S));
E:=IP(S);
END;
RETURN {M,E};
END;
TI-84 Plus CE Program TETRATION
"EWS
2018-08-14"
Disp "TETRATION
X^^Y","Y: INTEGER"
Prompt X,Y
10^(fPart(X))→M
iPart(log(X))→E
For(I,1,Y)
M*10^(E)*log(X)→S
10^(fPart(S))→M
iPart(S)→E
End
Disp
M,"*10^",E
Source:
“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
Eddie
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