There are a lot of Collatz Conjecture projects on Scratch (do a Scratch search) but very few offer any analysis. The Collatz Conjecture is one of the great, unsolved problems in mathematics and many believe a proof or counter-example is 'beyond mathematics'. Still, one can continue to search for patterns. Think of the powers of 2 as the trunk of a tree with 1 at the base and 2, 4, 8, 16, 32, 64 etc. climbing up the trunk. If N ever becomes a power of 2, then N cascades down the powers of 2 to bottom out at 1. The positive integers up to 1,152,921,504,606,846,975 have all been shown to enter the 4—2—1 loop. This means, that at some iteration, N must hit the tree trunk. Question 1: We know that if N = 1, N enters the 4-2-1 loop. How can one compute the value of N so that N immediately hits the tree trunk and cascades down the trunk? [I have listed the firs 6 values for N on the project screen.] Question 2: Is there a pattern in the sequence of Ns that immediately hit the trunk? Question 3: What condition must n, in 2^n, meet for N to hit the trunk immediately?
My other Collatz Projects The Collatz Conjecture—an Introduction https://scratch.mit.edu/projects/15709130/ Graph N vs. Number of Steps https://scratch.mit.edu/projects/118589334/ Graph of N vs. Orbit https://scratch.mit.edu/projects/118065441/
