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 $3\uparrow\uparrow\uparrow 3=\underbrace{{3}^{{3}^{\cdot^{\cdot^{\cdot^{3}}}}}\!\!}_{7,625,597,484,987}$ .

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.