A019916 Decimal expansion of tan(Pi/10) (angle of 18 degrees).

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

Offset

0,1

Comments

In a regular pentagon inscribed in a unit circle this is the cube of the length of the side divided by 5: (1/5)*(sqrt(3 - phi))^3 with phi from A001622. - Wolfdieter Lang, Jan 08 2018

Quartic number of denominator 5 and minimal polynomial 5x^4 - 10x^2 + 1. - Charles R Greathouse IV, May 13 2019

Links

Ivan Panchenko, Table of n, a(n) for n = 0..1000

Wikipedia, Exact trigonometric constants

Formula

Equals A019827/A019881 = 1/A019970 = 1/sqrt(5+2*sqrt(5)). - R. J. Mathar, Jul 26 2010

Equals tan((phi - 1)/sqrt(2 + phi)) = (1/5)*(sqrt(3 - phi))^3 = (3 - phi)*sqrt(3 - phi)/5 = sqrt(7 - 4*phi)/(2*phi - 1), with phi from A001622. - Wolfdieter Lang, Jan 08 2018

Equals Product_{k>=0} ((5*k + 1)/(5*k + 4))^(-1)^(k) = Product_{k>=0} A090771(k)/A090773(k). - Antonio Graciá Llorente, Mar 24 2024

Example

0.3249196962329063261558714122151344649549034715214751003078047191...

Mathematica

RealDigits[Tan[18 Degree], 10, 120][[1]] (* Harvey P. Dale, Mar 07 2012 *)

Prog

(PARI) tan(Pi/10) \\ Michel Marcus, Jan 08 2018

Crossrefs

Cf. A001622, A019827 (sin(Pi/10)), A019881 (cos(Pi/10)).

Sequence in context: A084657 A171559 A300883 * A201838 A099257 A325909

Adjacent sequences: A019913 A019914 A019915 * A019917 A019918 A019919

Keyword

nonn,cons

Author

N. J. A. Sloane

Status

approved