Boogafive

Boogafive is equal to \(5\uparrow\uparrow\uparrow5\), or 5 pentated to 5.
Googology Wiki user Hyp cos calls this number pentro, and it's equal to s(5,5,3) = s(5,2,4) = s(5,3,1,2) in strong array notation.Numbers from linear array notation | Steps Toward Infinity!
Googology Wiki user HaydenTheGoogologist2009 calls this number Hayden's Tripent, and it's equal to 5(5)5 in Hayden's Array Notation.Hayden's Big Numbers. Retrieved 2022-04-19.
== Etymology ==
The name "boogafive" is formed by adding the booga- prefix to 5.
The name "pentro" is based on the word "penta" and "tri" (Greek for 5 and 3), meaning a base-5 number, generated using hyper-3 operation based on exponentiation.
== Computation ==
Boogafive can be computed in the following process:
*\(f(1)=5\)
*\(f(2)=5^5=3,125\)
*\(f(3)=5^{5^5}\approx1.911\times10^{2,184}\)
*\(f(4)=5^{5^{5^5}}\)
*etc.
*Boogafive is equal to \(f(f(f(f(5))))\).
== Approximations ==
== Sources ==
== See also ==
Category:Numbers
Category:Up-arrow notation level
Category:3 entry linear
Category:Powers of 5
Category:Pentation
Category:Booga-