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%I M4466 #49 Aug 21 2023 11:25:41
%S 1,8,1,7,1,2,0,5,9,2,8,3,2,1,3,9,6,5,8,8,9,1,2,1,1,7,5,6,3,2,7,2,6,0,
%T 5,0,2,4,2,8,2,1,0,4,6,3,1,4,1,2,1,9,6,7,1,4,8,1,3,3,4,2,9,7,9,3,1,3,
%U 0,9,7,3,9,4,5,9,3,0,1,8,6,5,6,4,7,1,4
%N Decimal expansion of cube root of 6.
%C Diameter of a sphere with volume Pi. - _Omar E. Pol_, Aug 09 2012
%C Also the height h that minimizes the total surface area (including the base) of a square pyramid of unit volume: at h = 6^(1/3), the surface area reaches its minimum value, 12*6^(-1/3) = 12/h. The ratio of its height to the length of one of its sides is h/sqrt(3/h) = sqrt(2), and the slope of its four triangular faces is arctan(sqrt(8)) = 70.528779... degrees (cf. A137914). (For the height that minimizes the total surface area of just the four triangular faces of a square pyramid of unit volume -- i.e., excluding the base -- see A319034.) - _Jon E. Schoenfield_, Nov 10 2018
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Harry J. Smith, <a href="/A005486/b005486.txt">Table of n, a(n) for n = 1..20000</a>
%H <a href="/index/Al#algebraic_06">Index entries for algebraic numbers, degree 6</a>
%e 1.81712059283213965889121175632726050242821....
%t RealDigits[N[6^(1/3), 200]] (* _Vladimir Joseph Stephan Orlovsky_, May 27 2010 *)
%o (PARI) default(realprecision, 20080); x=6^(1/3); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b005486.txt", n, " ", d)); \\ _Harry J. Smith_, May 07 2009
%o (Magma) SetDefaultRealField(RealField(100)); 6^(1/3); // _G. C. Greubel_, Nov 12 2018
%Y Cf. A002949 = Continued fraction. - _Harry J. Smith_, May 07 2009
%Y Cf. A137914, A319034.
%K nonn,cons
%O 1,2
%A _N. J. A. Sloane_
%E More terms from _Jon E. Schoenfield_, Mar 11 2018
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