A232735 Decimal expansion of the real part of I^(1/7), or cos(Pi/14).

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, 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, 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

Offset: 0

Author

Stanislav Sykora, Nov 29 2013

Keywords

• nonn
• cons
• easy
• changed

Comments

The corresponding imaginary part is in A232736.

Root of the equation -7 + 56*x^2 - 112*x^4 + 64*x^6 = 0. - Vaclav Kotesovec, Apr 04 2021

Examples

			0.974927912181823607018131682993931217232785800619997437648...
		

Links

• Stanislav Sykora, Table of n, a(n) for n = 0..1000
• A. Arman, A. Bondarenko, and A. Prymak, Convex bodies of constant width with exponential illumination number, arXiv:2304.10418 [math.MG], 2023.
• Index entries for algebraic numbers, degree 6

Crossrefs

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))).

Programs

Magma

R:= RealField(100); Cos(Pi(R)/14); // G. C. Greubel, Sep 19 2022

Mathematica

RealDigits[Cos[Pi/14],10,120][[1]] (* Harvey P. Dale, Dec 15 2018 *)

SageMath

numerical_approx(cos(pi/14), digits=120) # G. C. Greubel, Sep 19 2022

Formula

2*this^2 -1 = A073052. - R. J. Mathar, Aug 29 2025

Equals 2F1(-1/14,1/14;1/2;1) . - R. J. Mathar, Aug 31 2025