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A005486
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Decimal expansion of cube root of 6.
(Formerly M4466)
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9
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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, 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, 0, 9, 7, 3, 9, 4, 5, 9, 3, 0, 1, 8, 6, 5, 6, 4, 7, 1, 4
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OFFSET
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1,2
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COMMENTS
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Diameter of a sphere with volume Pi. - Omar E. Pol, Aug 09 2012
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
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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EXAMPLE
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1.81712059283213965889121175632726050242821....
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MATHEMATICA
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PROG
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(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
(Magma) SetDefaultRealField(RealField(100)); 6^(1/3); // G. C. Greubel, Nov 12 2018
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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