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 <[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]>> 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]>> 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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