collatz

Collatz

A collatz sequence, starting with a positive integern, is found by repeatedly applying the following function to n until n == 1 :

 n = { n / 2 for even n ;
      3n + 1 for odd n }

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A more detailed description of the collatz conjecture may be found on Wikipedia.

The Problem

Create a function collatz that returns a collatz sequence string starting with the positive integer argument passed into the function, in the following form:

"X₀->X₁->...->X_N"

Where X_i is each iteration of the sequence and N is the length of the sequence.

Sample Input

Collatz.collatz(2) // should return "2->1"
Collatz.collatz(3) // should return "3->10->5->16->8->4->2->1"
Collatz.collatz(4) // should return "4->2->1"

Don't worry about invalid input. Arguments passed into the function are guaranteed to be valid integers >= 1.