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Joyce's pentatri is equal to \(\text g(3,1,1,4,3,3)\) in Joyce's More Generalized Exponential Notation.[1][2] The value was created by Andre Joyce as a failed attempt to define the Bowersism pentatri, which is even larger. In arrow notation, it is equal to 3^^^^(Joyce's tetratri-1 ^'s)^^^^^3. This number is closer to tritriplexian.

Approximations

Notation Approximation
BEAF {3,3,{3,3,{3,3,3}-1}-1} (exact)
Hyper-E notation E3##3#3
Chained arrow notation 3→3→3→2
Fast-growing hierarchy \(f^2_{\omega}(f_4(3))\)
Hardy hierarchy \(H_{\omega^{\omega}\times 2 + \omega^4}(3)\)
Slow-growing hierarchy \(g_{\Gamma_0}(3)\)

Sources

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