https://github.com/nqpz/mult3plus1

https://github.com/nqpz/mult3plus1

Last synced: 26 days ago
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• Host: GitHub
• URL: https://github.com/nqpz/mult3plus1
• Owner: nqpz
• License: other
• Created: 2019-10-09T18:18:29.000Z (about 5 years ago)
• Default Branch: master
• Last Pushed: 2024-07-26T16:30:46.000Z (3 months ago)
• Last Synced: 2024-07-26T18:21:59.427Z (3 months ago)
• Language: Haskell
• Homepage:
• Size: 75.2 KB
• Stars: 0
• Watchers: 3
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: COPYING

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README

        
# mult3plus1

I sometimes try to prove [the Collatz

conjecture](https://en.wikipedia.org/wiki/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 exec 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 exec 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.