nqpz / mult3plus1

mult3plus1

I sometimes try to prove the Collatz conjecture by programming my way out of it, but have not succeeded yet.

symbolic

This program calculates the tree of what infinite subparts need to be proved in order to prove that an integer $N > 1$ will always get smaller when run through the calculation of the conjecture.

Try running stack run mult3plus1-symbolic with one of these arguments:

• graph N: Print the tree as a GraphViz dot graph.

• successrate N: Print the percentage of successes.

• averagebranchingfactor N: Print the average branching factor.

• depthfirst: Do a depth-first search and print how many steps it takes to prove each subpart.

• depthfirstdelta: Same as depthfirst, but print the deltas between the integers. All deltas are probably positive.

• depthfirstdelta fibratio N: The ratio of numbers in the delta that are Fibonacci numbers. Seems pretty high (seems to reach 2 for larger values).

• depthfirstdelta fibratio comparerandom SEED: Run fibratio on both the Collatz proof tree and on a random tree to compare the two ratios.

Where $N$ is a positive integer denoting search depth.

modulo

Try running stack run mult3plus1-modulo N, where N is a positive integer. This program will try to find the fraction of all integers greater than 1 modulo $2^{N+1}$ that are guaranteed to become smaller when run through the calculation of the conjecture. The idea is that if all these integers can be shown to have this property (unlikely), then they will all end up at the integer 1 at the end, and the conjecture is proven.