Problem 52422. 3n + 1 Problem (a.k.a The Collatz Conjecture)

Sylvain Boutros

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The 3n + 1 problem (a.k.a The Collatz Conjecture)
Consider the following algorithm to generate a sequence of numbers. Start with an integer n. If n is even, divide by 2. If n is odd, multiply by 3 and add 1. Repeat this process with the new value of n, terminating when n = 1. For example, the following sequence of numbers will be generated for n = 22:
                    22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1
For an input n, the cycle-length of n is the number of numbers generated up to and including the 1. In the example above, the cycle length of 22 is 16. Given any two numbers i and j, you are to determine the maximum cycle length over all numbers between i and j, including both endpoints.
Input
The input will consist of a series of pairs of integers i and j, one pair of integers per line. All integers will be greater than 0.
Output
For each pair of input integers i and j, output a vector with i, j in the same order in which they appeared in the input and then the maximum cycle length for integers between and including i and j.
% Sample Input                    Sample Output
% 1 10                            [1, 10, 20]
% 100 200                         [100, 200, 125]   
% 201 210                         [201, 210, 89]
% 900 1000                        [900, 1000, 174]