The Collatz conjecture states that preforming the operation "multiply n by 3 and add 1 if it is odd, or half it if is even" will always eventually reach the final value of 1 (before looping indefinitely between 1, 4 and 2). This has been shown to be true for many values of n, but the general conjecture remains unproven. This tree diagram represents the possible sets of operations a sequence can take to get from its starting value to 1 (which is specified as the root node) for a set list of values of n (from 2 to N). A right turn in the direction facing away from 1 (the root node) indicates "n ->2n", and a left turn indicates "n -> (2n-1)/3".