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Ackermann Number

A number of the form n^...^_()_(n)n, where Knuth up-arrow notation has been used. The first few Ackermann numbers are 1^1=1, 2^^2=4, and 3^^^3=3^(3^(·^(·^(·^3))))_()_(7625597484987).

See also

Ackermann Function, Knuth Up-Arrow Notation, Power Tower

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References

Ackermann, W. "Zum hilbertschen Aufbau der reellen Zahlen." Math. Ann. 99, 118-133, 1928.Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 60-61, 1996.Crandall, R. E. "The Challenge of Large Numbers." Sci. Amer. 276, 74-79, Feb. 1997.Vardi, I. Computational Recreations in Mathematica. Redwood City, CA: Addison-Wesley, pp. 11, 227, and 232, 1991.

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Ackermann Number

Cite this as:

Weisstein, Eric W. "Ackermann Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AckermannNumber.html

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