Hold the 1 fixed. Notice in both sequences the remaining numbers are 3 interleaved ordered sets, in multiples of 2. Then watch this (just happened to post it two hours ago too)...
"Times Tables, Mandelbrot and the Heart of Mathematics" [video] https://www.youtube.com/watch?v=qhbuKbxJsk8
https://news.ycombinator.com/item?id=20558797
NB: And once again we find cycloids hiding underneath it all.
succ(x) = (x^2 + 2x) / (x^2 + 1). Newton's method [0]
~> Decimal expansion converges quadratically
0.618... = [0;1,1,1,1,...]. Continued fraction grows by (+1)/
0.618..., 1.0, 1.618..., 2.618.... Powers of Phi.
φ^2 = φ + 1
e^iτ = 0 + 1. Euler's identity (τ version) [1]
~> The complex exponential of the circle constant is unity.
Geometrically, multiplying by e^iθ corresponds to rotating a
complex number by an angle θ in the complex plane, which
suggests a second interpretation of Euler’s identity:
~> A rotation by one turn is 1.
√φ ≈ 4/π. Maybe a coincidence, maybe not.
0.283... = 2 * (π - 3.00)
[1] tau https://tauday.com/tau-manifesto#sec-euler_s_identity