Conversation

As an experiment, I asked #ChatGPT to write #Python code to compute, for each 𝑛, the length 𝑀(𝑛) of the longest subsequence of \(1,\dots,n\) on which the Euler totient function ϕ is non-decreasing. For instance, 𝑀(6)=5, because ϕ is non-decreasing on 1,2,3,4,5 (or 1,2,3,4,6) but not 1,2,3,4,5,6. Interestingly, it was able to produce an extremely clever routine to compute the totient function (that I had to stare at for a few minutes to see why it actually worked), but the code to compute \(M(n)\) was slightly off: it only considered subsequences of consecutive integers, rather than arbitrary subsequences. Nevertheless it was close enough that I was able to manually produce the code I wanted using the initial GPT-produced code as a starting point, probably saving me about half an hour of work. (and I now have the first 10,000 values of \(M\)). The results were good enough that I would likely turn to GPT again to provide initial code for similar calculations in the future. https://chat.openai.com/share/a022e1d6-dddc-4817-8bbd-944a3e742d9f