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Monthly Archives: April 2018
Iterating squared digit sum
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 digit, loop, Porges, proof, squared, sum
12 Comments
The chromatic number of the plane, part 1
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
More on sums of palindromes
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 followup post is that Lewis Baxter sent me the Python … Continue reading
Every positive integer is a sum of three palindromes
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 algorithm, constructive, news, palindromes, proof, sum
14 Comments
Why drawing orthogons is hard
We’re nearing the end of this little diversion on orthogons. We now know that orthogons are in 11 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 constraint, drawing, global, local, orthobraces, orthogonal, orthogons
3 Comments