Continuing our exploration of Collatz-like sequences

Yesterday my younger son and I did a fun project inspired by this blog post from Stephen Wolfram:

Introducing the 4n+2, 7n+1 problem: a less biased analog of the 3n+1 problem. Does 469 never terminate?https://t.co/ba0qHHTmsp pic.twitter.com/q8dmTOBTZr

— Stephen Wolfram (@stephen_wolfram) March 4, 2021

That project is here:

https://mikesmathpage.wordpress.com/2021/03/06/playing-with-the-collatz-conjecture-inspired-by-a-stephen-wolfram-blog-post/

Today we continued our exploration and started with a quick look at the 5n+1 problem we finished with yesterday:

Next we moved on to the mod 3 version that Stephen Wolfram looks at in his blog post.

Finally, we looked at what happens for the number 469 in this version of the Collatz conjecture, and talked through some ideas about how we would study if it ever repeats.

This was a fun exploration with my younger son. Wolfram’s blog post is incredible, but also accessible to kids. I love being able to explore ideas like these with kids.