[FRIAM] Nick being irritating --

[glen]

I figured it was one of these:

https://oeis.org/search?q=1%2C3%2C4%2C6%2C8%2C9%2C10%2C13%2C15&language=english&go=Search
https://oeis.org/search?q=1%2C3%2C5%2C6%2C8%2C10%2C12%2C13%2C15&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 <jonzingale at gmail.com <mailto:jonzingale at gmail.com>> 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 <thompnickson2 at gmail.com <mailto:thompnickson2 at gmail.com>> wrote:
> 
>         Sry. Should be all commas.
> 
> 
>         Sent from my Dumb Phone
> 
>         On Sep 9, 2025, at 1:19 PM, Nicholas Thompson <thompnickson2 at gmail.com <mailto:thompnickson2 at gmail.com>> 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.
> 
>         Please dont trouble yourself with this if you have anything better to do.
> 


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