Dear, Yuri: actually, you are posing problems, relationships that have to do a lot with the great role of number theory in future quantum theory of unification of the forces, including gravity.
The topic is to discuss so widespread, but in relation to this interesting pattern, maybe I can bring you something to help you.
First: it is easy to show that consecutive Fibonacci numbers, in particular, the first six numbers of the infinite series, Fibonacci, play a crucial role in the future unified theory, to develop.
Often apparent minor details, great keys to open locked doors.
The first six Fibonacci numbers, the number of divisors of nonzero roots of E8 group (eight dimensions), which is also the maximum amount of hyperspheres in 8d, touching each other to a central, ie kissing number (8d) = 240: 1, 1, 2, 3, 5, 8, 1 x 1 x 2 x 3 x 5 x 8 = 240
1 +1 +2 +3 +5 +8 = 20
[math](360^{\circ})/{\displaystyle \sum_{F_{n}/240}F_{n}=18^{\circ}}[/math]
[math]2\cdot\sin(18^{\circ})+1=\lim_{F_{n}\rightarrow\infty}(F_{n+1}/F_{n})=\varphi
[/math]
[math][2+\sin(2\pi/\sum_{F_{n}/240}F_{n})]^{2}=5.33155948031[/math]
[math]\exp([2+\sin(2\pi/\sum_{F_{n}/240}F_{n})]^{2})+\varphi^{-10}=206.768291888\simeq m_{\mu}/m_{e}[/math]
[math]m_{\mu}/m_{e}=206.7682843[/math]
[math]value\; vaccum\; Higgs=246.221202\; Gev=V(H)[/math]
[math]m_{h}=mass\; Higss\: boson\simeq V(H)/(1+\cos18^{\circ})=126.1989\; Gev
[/math]
2) The sequence you, Yuri, has discovered, seems to correspond to oscillations fixed at an angle of forty-five degrees (angle very important in physics, as you know very well) with a phase change corresponding to the angle shown in the above equations.
Even: this angle could correspond to a regularization with the unification angle, theories SU (5):
[math]\theta_{W}(GUT)=\arcsin(\sqrt{3/8})=37.7612^{\circ}
[/math]
3) As you know, an experiment has already shown the apparition of the golden ratio, underlying the group E8
a) http://physicsworld.com/cws/article/news/2010/jan/08/e8-symmetry-spotted-in-ultracold-magnet
b) www.tony5m17h.net/E8UniverseChain.pdf
Very interesting, really, its discovery.
Thank you so much¡
