Great to hear from you Matteo,
I have no idea mathematically what 1,3,4,6,8,11,10; is, but musically its the first 7 notes of "if I had a ribbon bow" (https://www.youtube.com/watch?v=rkXwfsGBupM). In that case the completion would be, 6,8,8, 8, 8, 8; But what is it really? N On Wed, Sep 10, 2025 at 10:45 AM Matteo Morini <[email protected] <mailto:[email protected]> > wrote: Then, I raise you 1,3,4,6,8,11,10 ! On 9/10/25 4:39 PM, Nicholas Thompson wrote: Yes. Thank you. I was beginning to fear i had asked an unfair q. Gpt got it on the first pass and then went on to say some interesting things about mathematics and semantics Sent from my Dumb Phone On Sep 10, 2025, at 10:25 AM, Matteo Morini <mailto:[email protected]> <[email protected]> wrote: (Western) music involved? A C major and a mystery, possibly minor, scale respectively? On 9/10/25 4:10 PM, Nicholas Thompson wrote: Next number in both series is one. Sent from my Dumb Phone On Sep 10, 2025, at 9:42 AM, Roger Frye <mailto:[email protected]> <[email protected]> wrote: Von Neuman warned against high degree polynomial fitting. He said "With four parameters I can fit an elephant, and with five I can make him wiggle his trunk.” <https://en.wikipedia.org/wiki/Von_Neumann's_elephant> Von Neumann's elephant <https://en.wikipedia.org/wiki/Von_Neumann's_elephant> en.wikipedia.org <https://en.wikipedia.org/wiki/Von_Neumann's_elephant> <https://en.wikipedia.org/wiki/Von_Neumann's_elephant> <wikipedia.png> On Sep 10, 2025, at 7:08 AM, glen <mailto:[email protected]> <[email protected]> wrote: I figured it was one of these: https://oeis.org/search?q=1%2C3%2C4%2C6%2C8%2C9%2C10%2C13%2C15 <https://oeis.org/search?q=1%2C3%2C4%2C6%2C8%2C9%2C10%2C13%2C15&language=english&go=Search> &language=english&go=Search https://oeis.org/search?q=1%2C3%2C5%2C6%2C8%2C10%2C12%2C13%2C15 <https://oeis.org/search?q=1%2C3%2C5%2C6%2C8%2C10%2C12%2C13%2C15&language=english&go=Search> &language=english&go=Search Were it so, we'd need the next number {16,17} to tell the difference. But like many of Nick's riddles, I have no idea what he intended. On 9/9/25 8:40 PM, Jon Zingale wrote: Sorry, 22. I needed to constrain the two systems. Too much linear algebra to want to explain, but yeah, Vandermonde and all that. On Tue, Sep 9, 2025 at 9:22 PM Jon Zingale <[email protected] <mailto:[email protected]> <mailto:[email protected]> <mailto:[email protected]>> wrote: It's 29. I am assuming you are thinking of a polynomial that generates each sequence. Unfortunately, it's a 6th degree polynomial and so solving for the coefficients is a pain. You construct a Vandermonde matrix (V) a vector of dummy coefficients a = [a0, a1, ..., a6]. Then you solve for the coefficients relative to your sequence (S), V * a = S. Python helped nicely: import numpy as np n1 = np.array([0, 1, 2, 3, 4, 5, 6]) y1 = np.array([1, 3, 5, 6, 8, 10, 12]) coeffs1 = np.polyfit(n1, y1, 6) sol1 = np.polyval(coeffs, 7) n2 = np.array([0, 1, 2, 3, 4, 5, 6]) y2 = np.array([1, 3, 4, 6, 8, 9, 10]) coeffs2 = np.polyfit(n2, y2, 6) sol2 = np.polyval(coeffs, 7) =>29 On Tue, Sep 9, 2025 at 3:17 PM Nicholas Thompson <[email protected] <mailto:[email protected]> <mailto:[email protected]> <mailto:[email protected]>> wrote: Sry. Should be all commas. Sent from my Dumb Phone On Sep 9, 2025, at 1:19 PM, Nicholas Thompson <[email protected] <mailto:[email protected]> <mailto:[email protected]> <mailto:[email protected]>> wrote: Here are two mathematical series 1,3,5,6,8,10.12, __ 1.3.4,6,8,9,10, __ Both have the same next number. Why, and what are we talking about here? I predict that only Jon will guess the answer. 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