This problem defines the Calkin-Wilf-Newman sequenceof positive rational numbers. The

Chapter 9, Problem 60

(choose chapter or problem)

This problem defines the Calkin-Wilf-Newman sequenceof positive rational numbers. The sequence is remarkablebecause every positive rational number appears as oneof its terms and none appears more than once. Every realnumber x can be written as an integer A plus a number Bwhere 0 B < 1. For example, for x = 12/5 = 2+2/5we have A = 2 and B = 2/5. For x = 3= 3+0 wehave A = 3 and B = 0. Define the function f(x) byf(x) = A + (1 B).For example, f(12/5) = 2 + (1 2/5) = 13/5 andf(3) = 3 + (1 0) = 4.(a) Evaluate f(x) for x = 25/8, 13/9, and .(b) Find the first six terms of the recursively definedCalkin-Wilf-Newman sequence: sn = 1/f(sn1)for n > 1 and s1 = 1.