A005486 Decimal expansion of cube root of 6.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• cons

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

Examples

			1.81712059283213965889121175632726050242821....
		

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

Crossrefs

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

Cf. A137914, A319034.

Programs

Magma

SetDefaultRealField(RealField(100)); 6^(1/3); // G. C. Greubel, Nov 12 2018

Mathematica

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

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

Extensions

More terms from Jon E. Schoenfield, Mar 11 2018