Here you will find my proposed proofs for the standard Syracuse conjecture (3n+1), as well as for some extensions (3n+b, 5n+1), and responses to the document arXiv2107.11160v4.

1. Slideshow in PDF format of the key steps of the proof of the "3n+1" conjecture (see it before reading full proof)
2. Direct access to the PDF files and tests (for those who already have a PDF)

These documents (internal version 4.3) are in the preprint stage

• Any feedback that could help improve the writing or simply correct a typo is welcome
• The next step is to use a proof assistant (COQ,...) to validate/refute the method
• I have taken care to sign the documents:
  • In Adobe Reader, you can view the signatures of the PDF files
  • A more thorough compliance check (including ZIP archives) can be performed on the site https://ec.europa.eu/digital-building-blocks/DSS/webapp-demo/validation
• The documents have also been deposited on the site https://www.copyright.eu
• The documents have also been deposited on the site https://www.zenodo.org
  • A Combinatorial Proof of the Syracuse Conjecture Using Transition Lists
  • Sequence of Syracuse : Extensions of types 3n+b and 5n+1
  • Answers to questions about the Syracuse sequence
• The documents are available under the CC BY-NC-ND 4.0 license

Jacques BALLASI ORCID : 0009-0002-7344-0608
You can contact me at the following address :