A343060 Decimal expansion of tan(Pi/16).

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

Offset

0,2

Comments

Smallest positive of the 4 real-valued roots of x^4+4*x^3-6*x^2-4*x+1=0 (Other: tan(5*Pi/16) = 1.49660.., -tan(7*Pi/16) = -5.027339.., -tan(3*Pi/16)= -0.6681786...) - R. J. Mathar, Sep 06 2025

Links

Table of n, a(n) for n=0..115.

Wikipedia, Trigonometric constants expressed in real radicals

Index entries for algebraic numbers, degree 4.

Formula

Equals sqrt( (2-sqrt(2+sqrt(2)))/(2+sqrt(2+sqrt(2))) ).

Equals sqrt(4+2*sqrt(2))-sqrt(2)-1.

Equals A182168/(1+A144981). - R. J. Mathar, Sep 06 2025

Example

0.19891236737965800691159762264...

Mathematica

RealDigits[Tan[Pi/16], 10, 100][[1]] (* Amiram Eldar, Apr 27 2021 *)

Prog

(PARI) tan(Pi/16)
(PARI) sqrt((2-sqrt(2+sqrt(2)))/(2+sqrt(2+sqrt(2))))
(PARI) sqrt(4+2*sqrt(2))-sqrt(2)-1

Crossrefs

Cf. A232738 (sin(Pi/16)), A232737 (cos(Pi/16)), A343057 (tan(Pi/32)).

Sequence in context: A090998 A163930 A157371 * A245330 A269222 A201994

Adjacent sequences: A343057 A343058 A343059 * A343061 A343062 A343063

Keyword

nonn,cons,easy

Author

Seiichi Manyama, Apr 04 2021

Status

approved