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%I #48 Jan 16 2024 16:51:22
%S 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,
%T 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,
%U 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
%N Decimal expansion of 2 + 2*sqrt(2).
%C Side length of smallest square containing five circles of radius 1. - _Charles R Greathouse IV_, Apr 05 2011
%C Equals n + n/(n +n/(n +n/(n +....))) for n = 4. See also A090388. - _Stanislav Sykora_, Jan 23 2014
%C Also the area of a regular octagon with unit edge length. - _Stanislav Sykora_, Apr 12 2015
%C The positive solution to x^2 - 4*x - 4 = 0. The negative solution is -1 * A163960 = -0.82842... . - _Michal Paulovic_, Dec 12 2023
%H G. C. Greubel, <a href="/A090488/b090488.txt">Table of n, a(n) for n = 1..10000</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Octagon">Octagon</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Regular_polygon">Regular polygon</a>
%H <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>
%F Equals 1 + A086178 = 2*A014176. - _R. J. Mathar_, Sep 03 2007
%F From _Michal Paulovic_, Dec 12 2023: (Start)
%F Equals A010466 + 2.
%F Equals A156035 - 1.
%F Equals A157258 - 5.
%F Equals A163960 + 4.
%F Equals A365823 - 2.
%F Equals [4; 1, 4, ...] (periodic continued fraction expansion).
%F Equals sqrt(4 + 4 * sqrt(4 + 4 * sqrt(4 + 4 * sqrt(4 + 4 * ...)))). (End)
%e 4.828427124746190097603377448419396157139343750...
%t RealDigits[2+2Sqrt[2],10,120][[1]] (* _Harvey P. Dale_, Mar 11 2015 *)
%o (PARI) 2*(1 + sqrt(2)) \\ _G. C. Greubel_, Jul 03 2017
%Y 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
%Y Cf. A002193, A010466, A014176, A086178, A156035, A157258, A163960, A365823.
%Y Cf. Areas of other regular polygons: A120011, A102771, A104956, A178817, A256853, A178816, A256854, A178809.
%K easy,nonn,cons
%O 1,1
%A _Felix Tubiana_, Feb 05 2004
%E Better definition from _Rick L. Shepherd_, Jul 02 2004
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