The numbers defined by the recurrence relation

with . The first few values for , 1, 2, ... are 1, 3, 3, 4, 7, 7, 7, 9, 9, 10, 13, ... (Sloane's A007448).

Conway and Guy (1996, p. 15) note that is the alphabetically first prime number if the American system of large number terminology, and term this "Knuth's number."

Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, p. 15, 1996.

Graham, R. L.; Knuth, D. E.; and Patashnik, O. Concrete Mathematics: A Foundation for Computer Science, 2nd ed. Reading, MA: Addison-Wesley, 1994.

Sloane, N. J. A. Sequence A007448/M2276 in "The On-Line Encyclopedia of Integer Sequences."

CITE THIS AS:

Weisstein, Eric W. "Knuth Number." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/KnuthNumber.html