I need your help, numbers that are built as follows... 2², 2³+3³, 2⁴+3⁴, 2⁵+3⁵+5⁵, 2⁶+3⁶+5⁶,...

[Davide Rotondo]

Hi to all, I don't know if I found something interesting. This is the link to the chatgpt discussion that I made. https://chatgpt.com/share/68e3687c-1274-8010-a990-56396ffbf763

See you soon

Davide

[Davide Rotondo]

In this link I also look for smallest k such that a(n) is divisible by (n+1)(n+3) https://chatgpt.com/share/68e3687c-1274-8010-a990-56396ffbf763

[Daniel Mondot]

Keep in mind that GPT in "chatGPT" means "Generative Pre-trained or Predictive Transformer". It is not a smart system, it only predicts the next word in a sentence based on its training. On a subject where limited information exists, it will regurgitate that, even if the source is satirical. And there has been examples of that. On a subject where there are no information available, it can allucinate anything. Now, it is true that chatGPT and other AI systems have recently become really good, but they can still make mistakes. So if you plan to coauthor a sequence with chatGPT, I suggest that you independently verify everything.

Daniel.

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[Davide Rotondo]

Thanks for the suggestion, I'll keep it in mind. What do you think about the chat gpt detection on my initiative?

Davide

To view this discussion visit https://groups.google.com/d/msgid/seqfan/CAD5iKai_oL%2BUQVgnwmV0r4_Tygv5b99G9mhV6-AnWqrGAP_oEQ%40mail.gmail.com.

[David desJardins]

On Mon, Oct 6, 2025 at 7:44 AM Daniel Mondot <dmo...@gmail.com> wrote:

Keep in mind that GPT in "chatGPT" means "Generative Pre-trained or Predictive Transformer". It is not a smart system, it only predicts the next word in a sentence based on its training.

That's true, but so do you. 

[David desJardins]

P.S. ChatGPT 5, Claude, Gemini, etc., don't only use a predictive model based on their training. They also retrieve relevant documents, perform side computations, and generally act in ways that a human assistant would, before answering questions.

[Arthur O'Dwyer]

On Mon, Oct 6, 2025 at 7:44 AM Daniel Mondot <dmo...@gmail.com> wrote:

Keep in mind that GPT in "chatGPT" means "Generative Pre-trained or Predictive Transformer". It is not a smart system, it only predicts the next word in a sentence based on its training. On a subject where limited information exists, it will regurgitate that, even if the source is satirical. And there has been examples of that. On a subject where there are no information available, it can allucinate anything. Now, it is true that chatGPT and other AI systems have recently become really good, but they can still make mistakes. So if you plan to coauthor a sequence with chatGPT, I suggest that you independently verify everything.

This subthread is off-topic, but... For a great example of how this "predicting the next word in a sentence" can go wrong in practice, I highly recommend this recent blog post doing a deep dive on the "seahorse emoji" meme:

https://vgel.me/posts/seahorse/

Back on-topic: I'm not competent to judge the ChatGPT output (nor does it terribly interest me), but in general Davide's posts here feel like "p-hacking." He just picks some formula, and looks through hundreds of correlations it might have (among the small numbers), and reports any time a positive correlation is found. But that's not interesting in a mathematical sense; in math we want to know causal connections that hold for all numbers, not just correlations that happen to exist for small numbers.

my $.02,

–Arthur