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]> wrote: > Sry. Should be all commas. > > > Sent from my Dumb Phone > > On Sep 9, 2025, at 1:19 PM, Nicholas Thompson <[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. > > > > Nick > Nicholas S. Thompson > Emeritus Professor of Psychology and Ethology > Clark University > [email protected] > https://wordpress.clarku.edu/nthompson >
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