Tripent

Tripent is equal to \(\lbrace5,5,5\rbrace\) or \(5\lbrace5\rbrace5\) in BEAF, \(5\uparrow\uparrow\uparrow\uparrow\uparrow5\) in arrow notation, or 5 heptated to 5.. The term was coined by Jonathan Bowers. This is the fifth Ackermann number.
Googology Wiki user Hyp cos calls this number a trienpent, and it's equal to s(5,5,5), s(5,2,6), s(5,5,1,2), s(5,1,1,3), or s(5,1,1,1,2) in strong array notation. Numbers from linear array notation | Steps Toward Infinity!
It can be computed during the following process:
# \(A(1)\) = 5
# \(A(2)\) = 5^5^5^5^5 (A(1) 5's)
# \(A(3)\) = 5^5^5^...5^5^5, with A(2) 5's.
# \(A(4)\) = 5^5^5^5^5^......5^5^5^5, with A(3) 5's
# Continue, let \(A(n)\) be 5^5^5^5^......^5^5^5 with \(A(n-1)\) 5's
# Tripent is . \(A^{A^{A^{A^{5}(1)}(1)}(1)}(1)\)
== Etymology ==
The name of this number is based on tri- (three) and penta- (five), meaning that there are 3 5's in the array.
==Approximations==
== Sources ==
== See also ==
* Tritri
Category:Numbers
Category:Numbers by Jonathan Bowers
Category:Up-arrow notation level
Category:3 entry linear
Category:Greek-based name
Category:BEAF
Category:Powers of 5
Category:Strong array notation numbers
ja:トリペント