Recursive Puzzle.js

/*
Consider this puzzle
------------------------------------------------------------
- Start from the number 1
- Repeatedly, either adding 5 or multiplying by 3, an infinite amount of new numbers can be produced.
- How would you write a function that, given a number, tries to find a sequence of such additions and multiplications that produce that number?
- For example, the number 13 could be reached by first multiplying by 3 and then adding 5 twice 
- Can number 15 be reached?
*/

function getPath(numAlpha) {
	function getNode(present, past) {
		if (present == numAlpha) {
			return past;
		}else if (present > numAlpha) {
			return null;
		}else{
			return getNode(present + 5, "(" + past + " + 5)") || getNode(present * 3, "(" + past + " * 3)");
		}
	}
	return getNode(1, "1");
}

console.log(getPath(24));