A₂ (Ackermann via hyper-operations)
What this is?
This page mirrors the case file definition:
A₂(x, y) = H(x, y+3, 2) − 3
with hyper‑operations H defined by
H(0,y,z)=y+1,
H(1,y,z)=y+z,
H(2,y,z)=y·z,
H(x≥3,0,z)=1,
H(x≥3,y>0,z): repeat y times result = H(x−1, result, z) starting from 1.
For z=2, this yields exponentiation for x=3 and tetration for x=4.
Answer
Demo queries (12)
Reason why
Closed forms: A₂(0,y)=y+1, A₂(1,y)=y+2, A₂(2,y)=2y+3, A₂(3,y)=2^(y+3)−3.
For x=4 we hit 2^^(y+3). When that’s still realistically printable (like 2^65536−3), we expand it exactly using a background worker.