A090488 Decimal expansion of 2 + 2*sqrt(2).

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

Offset: 1

Author

Felix Tubiana, Feb 05 2004

Keywords

• easy
• nonn
• cons

Comments

Side length of smallest square containing five circles of radius 1. - Charles R Greathouse IV, Apr 05 2011

Equals n + n/(n +n/(n +n/(n +....))) for n = 4. See also A090388. - Stanislav Sykora, Jan 23 2014

Also the area of a regular octagon with unit edge length. - Stanislav Sykora, Apr 12 2015

The positive solution to x^2 - 4*x - 4 = 0. The negative solution is -1 * A163960 = -0.82842... . - Michal Paulovic, Dec 12 2023

Examples

			4.828427124746190097603377448419396157139343750...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• Wikipedia, Octagon
• Wikipedia, Regular polygon
• Index entries for algebraic numbers, degree 2

Crossrefs

Cf. n+n/(n+n/(n+...)): A090388 (n=2), A090458 (n=3), A090550 (n=5), A092294 (n=6), A092290 (n=7), A090654 (n=8), A090655 (n=9), A090656 (n=10). - Stanislav Sykora, Jan 23 2014

Cf. A002193, A010466, A014176, A086178, A156035, A157258, A163960, A365823.

Cf. Areas of other regular polygons: A120011, A102771, A104956, A178817, A256853, A178816, A256854, A178809.

Programs

Mathematica

RealDigits[2+2Sqrt[2],10,120][[1]] (* Harvey P. Dale, Mar 11 2015 *)

PARI

2*(1 + sqrt(2)) \\ G. C. Greubel, Jul 03 2017

Formula

Equals 1 + A086178 = 2*A014176. - R. J. Mathar, Sep 03 2007

From Michal Paulovic, Dec 12 2023: (Start)

Equals A010466 + 2.

Equals A156035 - 1.

Equals A157258 - 5.

Equals A163960 + 4.

Equals A365823 - 2.

Equals [4; 1, 4, ...] (periodic continued fraction expansion).

Equals sqrt(4 + 4 * sqrt(4 + 4 * sqrt(4 + 4 * sqrt(4 + 4 * ...)))). (End)

Extensions

Better definition from Rick L. Shepherd, Jul 02 2004