Manuals/calci/PENTATE

PENTATE (a,n)

• $a$ and $n$ are any real numbers.

Description

• This function shows the value of Pentation of given numbers.
• In $PENTATE(a,n)$,$a$ and $n$ are any real numbers.
• Pentation is indicating the fifth hyper operator.
• The most common notation for pentate is used by Knuth's up-arrow notation as $a\uparrow \uparrow \uparrow b$ or $a\uparrow ^{3}b$ or a^^^b .
• It can also be notated a{3}b in Bowers operator notation.
• Normally notation can be continued for $a^{b}$ for exponents and $^{b}a$ for teteration and a(*)b for pentation.
• Pentation has the following properties:a^^(a^^^b) = a^^^(b+1), and (a^^^b)^^^c ~< a^^^(b+c).
• But other than that, it has even fewer nice properties than tetration has.
• Some examples of Pentation are given below:

1. 2^^^1 = 2^^(2^^0) = 2^^1 = 2.
2. 2^^^3 = 2^^2^^2 = 2^^4 = 2^2^2^2 = 2^2^4 = 2^16 = 65536

Examples

1. PENTATE(3,2) = 7625597484987
2. PENTATE(4,1) = 4
3. PENTATE(1,3) = 1
4. PENTATE(5,2) = Infinity

See Also

• TETRATE
• SLOG
• SUPERLOGARITHM

References

• Pentate

• List of Main Z Functions

• Z3 home