A005486 - OEIS

A005486

Decimal expansion of cube root of 6.
(Formerly M4466)

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

1,2

COMMENTS

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

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..20000

Index entries for algebraic numbers, degree 6

EXAMPLE

1.81712059283213965889121175632726050242821....

MATHEMATICA

RealDigits[N[6^(1/3), 200]] (* Vladimir Joseph Stephan Orlovsky, May 27 2010 *)

PROG

(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

CROSSREFS

Cf. A002949 = Continued fraction. - Harry J. Smith, May 07 2009

Cf. A137914, A319034.

Sequence in context: A240982 A258146 A182551 * A010157 A244089 A195489

Adjacent sequences: A005483 A005484 A005485 * A005487 A005488 A005489

KEYWORD

nonn,cons

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Jon E. Schoenfield, Mar 11 2018

STATUS

approved