
Need Solutions for Concrete Mathematics (Floors and Ceilings) Question 25 - MOmarFarooq
25) Prove or disprove that the Knuth numbers, dened by (3.16), satisfy Kn &gt;= n for all nonnegative n
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MOmarFarooq
Recurrence equation (3.16): k0=1, kn+1=1+min{2k⌊n/2⌋,3k⌊n/3⌋}(n≥0). Thus, for
example, k1 is 1+min(2k0,3k0)=3 and the sequence begins as
1,3,3,4,7,7,7,9,9,10,13,⋯ One of the authors of this book has modestly decided
to call these the Knuth numbers.

Exercise 25 asks for a proof or disproof that kn≥n, for all n≥0. The first few
k's just listed do satisfy the inequality, so there is a good chance that it
is true in general.

Your help will be appreciated!

