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%I #24 Apr 23 2023 22:34:14
%S 9,7,4,9,2,7,9,1,2,1,8,1,8,2,3,6,0,7,0,1,8,1,3,1,6,8,2,9,9,3,9,3,1,2,
%T 1,7,2,3,2,7,8,5,8,0,0,6,1,9,9,9,7,4,3,7,6,4,8,0,7,9,5,7,5,0,8,7,6,4,
%U 5,9,3,1,6,3,4,4,0,3,7,9,3,7,0,0,1,1,2,4,5,8,1,2,0,7,3,6,9,2,5,1,6,4,0,1,4
%N Decimal expansion of the real part of I^(1/7), or cos(Pi/14).
%C The corresponding imaginary part is in A232736.
%C Root of the equation -7 + 56*x^2 - 112*x^4 + 64*x^6 = 0. - _Vaclav Kotesovec_, Apr 04 2021
%H Stanislav Sykora, <a href="/A232735/b232735.txt">Table of n, a(n) for n = 0..1000</a>
%H A. Arman, A. Bondarenko, and A. Prymak, <a href="https://arxiv.org/abs/2304.10418">Convex bodies of constant width with exponential illumination number</a>, arXiv:2304.10418 [math.MG], 2023.
%e 0.974927912181823607018131682993931217232785800619997437648...
%t RealDigits[Cos[Pi/14],10,120][[1]] (* _Harvey P. Dale_, Dec 15 2018 *)
%o (Magma) R:= RealField(100); Cos(Pi(R)/14); // _G. C. Greubel_, Sep 19 2022
%o (SageMath) numerical_approx(cos(pi/14), digits=120) # _G. C. Greubel_, Sep 19 2022
%Y Cf. A232736 (imaginary part), A010503 (real(I^(1/2))), A010527 (real(I^(1/3))), A144981 (real(I^(1/4))), A019881 (real(I^(1/5))), A019884 (real(I^(1/6))), A232737 (real(I^(1/8))), A019889 (real(I^(1/9))), A019890 (real(I^(1/10))).
%K nonn,cons,easy
%O 0,1
%A _Stanislav Sykora_, Nov 29 2013
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