Monthly Archives: April 2018

Iterating squared digit sum

Posted on April 26, 2018 by Brent

Another fun fact I learned from John Cook. Let be the function which takes a positive integer and outputs the sum of the squares of its digits. For example, . Since the output is itself another positive integer, we can … Continue reading →

Posted in arithmetic, computation, proof | Tagged , , , , , | 12 Comments

The chromatic number of the plane, part 1

Posted on April 18, 2018 by Brent

About a week ago, Aubrey de Grey published a paper titled “The chromatic number of the plane is at least 5”, which is a really cool result. It’s been widely reported already, so I’m actually a bit late to the … Continue reading →

Posted in geometry, proof | Tagged , , , , | 4 Comments

More on sums of palindromes

Posted on April 11, 2018 by Brent

In my previous post I reported on a recent proof that every positive integer can be written as the sum of three palindromes. The first thing to report in this follow-up post is that Lewis Baxter sent me the Python … Continue reading →

Posted in arithmetic, computation, links | Tagged , , , | 7 Comments

Every positive integer is a sum of three palindromes

Posted on April 9, 2018 by Brent

I recently learned from John Cook about a new paper by Javier Cilleruelo, Florian Luca, and Lewis Baxter proving that every positive integer can be written as a sum of three palindromes. A palindrome is a number that is the … Continue reading →

Posted in arithmetic, computation, links | Tagged , , , , , | 14 Comments

Why drawing orthogons is hard

Posted on April 5, 2018 by Brent

We’re nearing the end of this little diversion on orthogons. We now know that orthogons are in 1-1 correspondence with orthobraces, and we can efficiently generate orthobraces. The only thing left is to find a way to turn orthobraces into … Continue reading →

Posted in computation, geometry | Tagged , , , , , , | 3 Comments