Kata

Preface

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

$f(n)=\{\begin{array}{c}n\mathrm{/}2,\text{ if }n\text{ is even}\\ 3n+1,\text{ if }n\text{ is odd}\end{array}f(n)\; =\; \backslash begin\{cases\}\; n/2,\; \backslash text\{\; if\; \$n\$\; is\; even\}\; \backslash \backslash \; 3n+1,\; \backslash text\{\; if\; \$n\$\; is\; odd\}\; \backslash end\{cases\}$

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

Input: 4
Output: "4->2->1"

Input: 3
Output: "3->10->5->16->8->4->2->1"

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