A387454 Decimal expansion of cos(Pi/21).

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

Offset

0,1

Comments

The 21st cyclotomic polynomial is 1-x+x^3-x^4+x^6-x^8+x^9-x^11+x^12 and has roots -this +- 0.14904226..*i, - 0.733051871.. +- 0.680172737..*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

Equals sin(19/42*Pi).

Largest of the 6 real-valued roots of 64*x^6+32*x^5-96*x^4-48*x^3+32*x^2+16*x+1=0.

4*this^3 -3*this = A073052.

Equals 2F1(-1/14,1/14;1/2;3/4). - R. J. Mathar, Aug 31 2025

Example

0.988830826225128545069742882934008613065251013574...

Mathematica

First[RealDigits[Cos[Pi/21], 10, 100]] (* Paolo Xausa, Nov 17 2025 *)

Crossrefs

Cf. A019688.

Sequence in context: A382604 A157680 A396759 * A305382 A347199 A011228

Adjacent sequences: A387451 A387452 A387453 * A387455 A387456 A387457

Keyword

nonn,cons,easy

Author

R. J. Mathar, Aug 29 2025

Status

approved