A010482 Decimal expansion of square root of 27.

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

Offset

1,1

Comments

Continued fraction expansion is 5 followed by {5, 10} repeated (A040021). - Harry J. Smith, Jun 04 2009

6 + sqrt(27) represents the surface of a dodecahedron of side equal to one. S = 3*a^2(2 + sqrt(3)) with a = 1. - Vincenzo Librandi, Jul 10 2010

sqrt(27) is the perimeter of an equilateral triangle whose incircle's diameter is 1. - Martin Janecke, May 31 2016

If r = 2*a * sin(3t)/sin(2t) and x*(x^2+y^2) = a * (3x^2-y^2) are respectively a polar equation and a Cartesian equation of the Maclaurin trisectrix, then sqrt(27) * a^2 = area of the loop of this trisectrix = area between the curve and its asymptote (see Mathcurve link). - Bernard Schott, Jul 14 2020

Area of a regular hexagon with side length sqrt(2). - Christoph B. Kassir, Sep 29 2022

The solution of x^sqrt(3)=sqrt(3)^x, see e.g. A360148. - R. J. Mathar, Mar 24 2023

Links

Harry J. Smith, Table of n, a(n) for n = 1..20000

Robert Ferréol, MacLaurin trisectrix, Mathcurve.

Index to sequences related to curves.

Index entries for algebraic numbers, degree 2

Formula

Equals 3*sqrt(3) = 3 * A002194. - Bernard Schott, Jul 14 2020

Equals 2 * A104956. - Christoph B. Kassir, Oct 02 2022

Example

5.196152422706631880582339024517617100828415761431141884167420938355799....

Mathematica

RealDigits[N[Sqrt[27], 200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Feb 22 2011 *)

Prog

(PARI)  default(realprecision, 20080); x=sqrt(27); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010482.txt", n, " ", d));  \\ Harry J. Smith, Jun 04 2009

Crossrefs

Cf. A040021 (continued fraction), A248254 (Egyptian fraction).

Cf. A104956 (half), A002194 (sqrt(3)).

Sequence in context: A198671 A129343 A342634 * A135856 A097414 A154605

Adjacent sequences: A010479 A010480 A010481 * A010483 A010484 A010485

Keyword

nonn,cons,easy

Author

N. J. A. Sloane

Status

approved