A387441 Decimal expansion of cos(Pi/13).

9, 7, 0, 9, 4, 1, 8, 1, 7, 4, 2, 6, 0, 5, 2, 0, 2, 7, 1, 5, 6, 9, 8, 2, 2, 7, 6, 2, 9, 3, 7, 8, 9, 2, 2, 7, 2, 4, 9, 8, 6, 5, 1, 0, 5, 7, 3, 9, 0, 0, 3, 5, 8, 8, 5, 8, 7, 6, 4, 4, 5, 2, 6, 4, 7, 7, 0, 4, 1, 7, 0, 8, 7, 6, 0, 0, 0, 6, 6, 7, 6, 9, 3, 2, 5, 7, 4, 6, 0, 6, 4, 0, 8, 3, 8, 4, 2, 6, 1, 5, 5, 4, 4, 3, 8, 2, 0, 5, 4, 9, 7, 5, 0, 0, 9, 9, 1, 9

Offset

0,1

Comments

The 13th cyclotomic polynomial is 1+x+x^2+..+x^12 and has the roots -this +- 0.239315664..*i, -0.748510748.. +- 0.663122658..*i, -0.354604887.. +- 0.935016242..*i, 0.120536680...+- A387446*i, etc. - R. J. Mathar, Jun 11 2026

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

R. J. Mathar, Reduction formulas of the cosine of integer fractions of pi, (2008) vixra:2210.0026.

Index entries for algebraic numbers, degree 6.

Formula

Largest of the 6 real-valued roots of 64*x^6 -32*x^5 -80*x^4 +32*x^3 +24*x^2 -6*x -1 = 0.

Equals sin(11/26*Pi).

Example

0.97094181742605202715698227629378922724986510573900...

Mathematica

First[RealDigits[Cos[Pi/13], 10, 100]] (* Paolo Xausa, Nov 18 2025 *)

Crossrefs

Cf. A019680.

Sequence in context: A145422 A341332 A021107 * A155691 A393087 A106727

Adjacent sequences: A387438 A387439 A387440 * A387442 A387443 A387444

Keyword

nonn,cons,easy

Author

R. J. Mathar, Aug 29 2025

Status

approved