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Knuth Number


The numbers defined by the recurrence relation

 K_(n+1)=1+min(2K_(|_n/2_|),3K_(|_n/3_|)),

with K_0=1. The first few values for n=0, 1, 2, ... are 1, 3, 3, 4, 7, 7, 7, 9, 9, 10, 13, ... (OEIS A007448).

Conway and Guy (1996, p. 15) note that 8018018851 is the alphabetically first prime number in the American system of large number terminology, and term this "Knuth's number."


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References

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."

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Knuth Number

Cite this as:

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

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