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A010464 Decimal expansion of square root of 6.

%I A010464 #66 Oct 19 2024 18:40:21
%S A010464 2,4,4,9,4,8,9,7,4,2,7,8,3,1,7,8,0,9,8,1,9,7,2,8,4,0,7,4,7,0,5,8,9,1,
%T A010464 3,9,1,9,6,5,9,4,7,4,8,0,6,5,6,6,7,0,1,2,8,4,3,2,6,9,2,5,6,7,2,5,0,9,
%U A010464 6,0,3,7,7,4,5,7,3,1,5,0,2,6,5,3,9,8,5,9,4,3,3,1,0,4,6,4,0,2,3
%N A010464 Decimal expansion of square root of 6.
%C A010464 Continued fraction expansion is 2 followed by {2, 4} repeated. - _Harry J. Smith_, Jun 05 2009
%C A010464 Ratio t*o/c^2 where t, o and c are respectively the edge lengths of a tetrahedron, an octahedron and a cube whose total surface areas are the same. See CNRS links. - _Michel Marcus_, Mar 03 2022 and Apr 21 2016
%C A010464 Diameter of a sphere whose surface area equals 6*Pi. More generally, the square root of x is also the diameter of a sphere whose surface area equals x*Pi. - _Omar E. Pol_, Aug 29 2024
%H A010464 Harry J. Smith, <a href="/A010464/b010464.txt">Table of n, a(n) for n = 1..20000</a>
%H A010464 Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/sqrt_base">Index of expansions of sqrt(d) in base b</a>
%H A010464 R. J. Nemiroff and J. Bonnell, Plouffe's Inverter, <a href="https://wayback.cecm.sfu.ca/projects/ISC/dataB/isc/C/sqrt6.txt">The first 1 million digits of the square root of 6</a>
%H A010464 R. J. Nemiroff and J. Bonnell, <a href="http://antwrp.gsfc.nasa.gov/htmltest/gifcity/sqrt6.1mil">The first 1 million digits of the square root of 6</a>
%H A010464 Ana Rechtman, <a href="http://images-archive.math.cnrs.fr/Avril-2016-2e-defi.html">Avril 2016, 2e défi</a>, Images des Mathématiques, CNRS, 2016.
%H A010464 Ana Rechtman, <a href="http://images-archive.math.cnrs.fr/Avril-2016-3e-defi.html?lang=fr">Avril 2016, 3e défi (Solution du 2e défi d’Avril)</a>, Images des Mathématiques, CNRS, 2016.
%H A010464 <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>
%F A010464 Equals A002193*A002194. - _Michel Marcus_, Apr 21 2016
%e A010464 2.449489742783178098197284074705891391965947480656670128432692567250960...
%e A010464 Sqrt(6) = sqrt(1+i*sqrt(3)) + sqrt(1-i*sqrt(3)), where i=sqrt(-1). - _Bruno Berselli_, Nov 20 2012
%t A010464 RealDigits[N[Sqrt[6],200]][[1]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 20 2011 *)
%o A010464 (PARI)  default(realprecision, 20080); x=sqrt(6); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010464.txt", n, " ", d));  \\ _Harry J. Smith_, Jun 01 2009
%o A010464 (PARI) sqrt(6) \\ _Michel Marcus_, Apr 21 2016
%o A010464 (Magma) SetDefaultRealField(RealField(100)); Sqrt(6); // _Vincenzo Librandi_, Feb 15 2020
%Y A010464 Cf. A002193 (sqrt(2)), A002194 (sqrt(3)).
%Y A010464 Cf. A040003 (continued fraction).
%K A010464 nonn,cons
%O A010464 1,1
%A A010464 _N. J. A. Sloane_