This problem defines the calkin wilf-newman sequence of

Question

Question: This problem defines the Calkin Wilf-Newman sequence of positive rational numbers. The sequence is remarkable because every positive rational number appears as one of its terms and none appears more than once. Every real number x can be written as an integer A plus a number B where 0 ≤ B

f(x) = A + (1 - B).

For example, f(12/5) = 2 + (1 - 2/5) = 13/5 and f(3) = 3 + (1 - 0) = 4.

(a) Evaluate f(x) for x = 25/8, 13/9, and π.

(b) Find the first six terms of the recursively defined Calkin-Wilf-Newman sequence: sn = 1/f(s_n-1) for n > 1 and s₁ = 1.