Ackermann and the superpowers

@article{Porto1980AckermannAT,
  title={Ackermann and the superpowers},
  author={Ant{\'o}nio Porto and Armando B. Matos},
  journal={SIGACT News},
  year={1980},
  volume={12},
  pages={90-95}
}
The Ackermann function a(m, n) is a classical example of a total recursive function which is not primitive recursive. It grows faster than any primitive recursive function. It is usually defined by a general recurrence together with two “boundary” conditions. In this paper we obtain a closed form of a(m, n), which involves the Knuth superpower notation, namely a(m, n) = 2 m−2 ↑ (n + 3) − 3. Generalized Ackermann functions, that is functions satisfying only the general recurrence and one of the… 

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