Manuals/calci/TETRATE

TETRATE(a,n)

• $a$ is the base value.
• $n$ is power value.

Description

• This function shows the tetration value of the given number.
• In $TETRATE(a,n)$,$a$ is the base value and $n$ is the power value.
• The hyperoperation after exponentiation is Tetration.
• Tetration is called iterated exponentiation.
• The notation $^{n}a$ means Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. TeX parse error: Double exponent: use braces to clarify"): {\displaystyle a^{a}^{\cdots }^{a}} the application of exponentiation $n-1$ times.
• For any positive real a>0 and non-negative integer $n\geq 0$ we define $^{n}a$by:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ^n a = \begin{cases} 1, & \mbox{if }n\mbox{=0} \\ a, & \mbox{if }n\mbox{ >0} \end{cases}}

$f(n)={\begin{cases}n/2,&{\mbox{if }}n{\mbox{ is even}}\\3n+1,&{\mbox{if }}n{\mbox{ is odd}}\end{cases}}$