Playing with the Collatz conjecture inspired by a Stephen Wolfram blog post

I saw a really neat blog post from Stephen Wolfram last week:

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

The blog post has so many different ideas that you could share with kids, but I decided to spend the weekend exploring various versions of Collatz-like sequences with my son.

We started by looking at some simple code in Mathematica to generate Collatz sequences:

Next we looked at how long it took various numbers to get to 1 in the Collatz sequence and looked at a histogram of the numbers. We got a fun surprise:

We wrapped up today’s project by looking at what happens when you replace the 3x + 1 rule in the Collatz conjecture with a 5x + 1 rule. I don’t remember ever seeing this idea before and it was one that really surprised me reading through Wolfram’s blog post this morning:

Tomorrow we’ll extend today’s project by looking at the 4x + 2 and 7x + 1 version that Stephen Wolfram mentioned in his tweet. Hopefully that’ll make for a really fun project, too.