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Ackermann Number

A number of the form \(n\underbrace{\uparrow\cdots\uparrow}_n n\), where Arrow Notation has been used. The first few Ackermann numbers are $1\uparrow 1=1$, $2\uparrow\uparrow 2=4$, and \(3\uparrow\uparrow\uparrow 3=\underbrace{{3}^{{3}^{\cdot^{\cdot^{\cdot^{3}}}}}\!\!}_{7,625,597,484,987}\).

See also Ackermann Function, Arrow Notation, Power Tower


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.

© 1996-9 Eric W. Weisstein