A319034 -id:A319034 - cp's OEIS frontend

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

N. J. A. Sloane

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

			1.81712059283213965889121175632726050242821....

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

Harry J. Smith, Table of n, a(n) for n = 1..20000
Index entries for algebraic numbers, degree 6

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

Cf. A137914, A319034.

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

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

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

More terms from Jon E. Schoenfield, Mar 11 2018

A358943 Decimal expansion of the real root of 3*x^3 - 2.

Original entry on oeis.org

8, 7, 3, 5, 8, 0, 4, 6, 4, 7, 3, 6, 2, 9, 8, 8, 6, 9, 0, 4, 7, 2, 2, 0, 4, 2, 6, 8, 1, 3, 9, 9, 8, 7, 5, 6, 7, 4, 6, 4, 7, 5, 8, 8, 1, 9, 0, 7, 8, 7, 7, 2, 4, 1, 7, 0, 0, 9, 2, 4, 6, 0, 1, 9, 0, 9, 5, 6, 6, 6, 0, 6, 3, 9, 8, 6, 8, 0

Offset: 0

Wolfdieter Lang, Jan 02 2023

This number is the reciprocal of A319034.

The other (complex) roots are, with the present number r = (2/3)^(1/3), r*w = -0.4367902323... + 0.7565428747...*i, and its conjugate, where w = exp(2*Pi*i/3) = (-1 + sqrt(3)*i)/2 is one of the complex roots of x^3 - 1.

			0.87358046473629886904722042681399875674647588190787724170092460190956...

Cf. A010590, A319034.

RealDigits[Surd[2/3, 3], 10, 100][[1]] (* Amiram Eldar, Jan 05 2023 *)

(2/3)^(1/3) \\ Michel Marcus, Jan 05 2023

r = (2/3)^(1/3) = 1/A319034 = (1/3)*18^(1/3) = (1/3)*A010590.

cp's OEIS Frontend

A005486 Decimal expansion of cube root of 6.

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