19683

19,683 is a number equal to (33)3 = 332 = 39 = 273. It can be written as \(3 \downarrow \downarrow 3\) in down-arrow notation, and therefore it shows up frequently when working with threes in down-arrow notation, analogous to 7,625,597,484,987 in up-arrow notation.
With the fuga- prefix, this number can be named "fugathree".
19,683 is a Dudeney number, that is it's digits add up to its cube root: 1+9+6+8+3 = 27, and 273 = 19,683. It is the largest base-10 Dudeney number (the others are 512, 4,913, 5,832, and 17,576).
==Approximation==
Notation 	Lower bound 	Upper bound
Scientific notation 	\(1.9683\times10^4\) 	\(1.9683\times10^4\)
Arrow notation 	\(3\uparrow9\) 	\(3\uparrow9\)
Steinhaus-Moser Notation 	5[3] 	6[3]
Copy notation 	1[5] 	2[5]
Taro's multivariable Ackermann function	A(3,11) 	A(3,12)
Pound-Star Notation 	#*(99)*2 	#*(100)*2
BEAF 	{3,9} 	{3,9}
Hyper-E notation 	E[3]9 	E[3]9
Bashicu matrix system 	(0)[140] 	(0)[141]
Hyperfactorial array notation 	7! 	8!
Fast-growing hierarchy 	\(f_2(10)\) 	\(f_2(11)\)
Hardy hierarchy 	\(H_{\omega^2}(10)\) 	\(H_{\omega^2}(11)\)
Slow-growing hierarchy 	\(g_{\omega^{\varepsilon_0+\omega2}}(3)\)	\(g_{\omega^{\varepsilon_0+\omega2}}(3)\)
==See also==
*Fugafour
Category:Numbers
Category:Class 1
Category:Numbers with 4 to 6 digits
Category:Powers of 3
Category:Fuga-