

A002580


Decimal expansion of cube root of 2.
(Formerly M1354 N0521)


26



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

1,2


COMMENTS

2^(1/3) is Hermite's constant gamma_3.  JeanFrançois Alcover, Sep 02 2014, after Steven Finch.
For doubling the cube using origami and a standard geometric construction employing two right angles see the W. Lang link, Application 2, p. 14, and the references given there. See also the L. Newton link.  Wolfdieter Lang, Sep 02 2014
Length of an edge of a cube with volume 2.  Jared Kish, Oct 16 2014
For any positive real c, the mappings R(x)=(c*x)^(1/4) and S(x)=sqrt(c/x) have the same unique attractor c^(1/3), to which their iterated applications converge from any complex plane point. The present case is obtained setting c=2. It is noteworthy that in this way one can evaluate cube roots using only square roots. The CROSSREFS list some other cases of cube roots to which this comment might apply.  Stanislav Sykora, Nov 11 2015


REFERENCES

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Horace S. Uhler, Manyfigure approximations for cubed root of 2, cubed root of 3, cubed root of 4, and cubed root of 9 with chi2 data. Scripta Math. 18, (1952). 173176.


LINKS

Harry J. Smith, Table of n, a(n) for n = 1..20000
Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 62.
Wolfdieter Lang, Notes on Some Geometric and Algebraic Problems solved by Origami, arXiv:1409.4799 [math.MG], 2014.
Liz Newton, The power of origami.
Simon Plouffe, Plouffe's Inverter, The cube root of 2 to 20000 digits
Simon Plouffe, 2**(1/3) to 2000 places
Simon Plouffe, Generalized expansion of real constants
H. S. Uhler, Manyfigure approximations for cubed root of 2, cubed root of 3, cubed root of 4, and cubed root of 9 with chi2 data, Scripta Math. 18, (1952). 173176. [Annotated scanned copies of pages 175 and 176 only]
Eric Weisstein's World of Mathematics, Delian Constant


FORMULA

(2^(1/3)  2^(1/3) * sqrt(3))^3 = (2^(1/3) + 2^(1/3) * sqrt(3))^3 = 16.  Alonso del Arte, Jan 04 2015
Set c=2 in the identities c^(1/3) = sqrt(c/sqrt(c/sqrt(c/...))) = sqrt(sqrt(c*sqrt(sqrt(c*sqrt(sqrt(...)))))).  Stanislav Sykora, Nov 11 2015
Equals Product_{k>=0} (1 + (1)^k/(3*k + 2)).  Amiram Eldar, Jul 25 2020


EXAMPLE

1.2599210498948731647672106072782283505702514...


MAPLE

Digits:=100: evalf(2^(1/3)); # Wesley Ivan Hurt, Nov 12 2015


MATHEMATICA

RealDigits[N[2^(1/3), 5!]] (* Vladimir Joseph Stephan Orlovsky, Sep 04 2008 *)


PROG

(PARI) { default(realprecision, 20080); x=2^(1/3); for (n=1, 20000, d=floor(x); x=(xd)*10; write("b002580.txt", n, " ", d)); } \\ Harry J. Smith, May 07 2009
(PARI) { default(realprecision, 100); x= 2^(1/3); for(n=1, 100, d=floor(x); x=(xd)*10; print1(d, ", ")) } \\ Altug Alkan, Nov 14 2015


CROSSREFS

Cf. A002945 (continued fraction), A253583.
Cf. A246644.  Wolfdieter Lang, Sep 02 2014
Cf. A002581, A005480, A005481, A005482, A005486, A010581, A010582, A092039, A092041, A139340.  Stanislav Sykora, Nov 11 2015
Sequence in context: A020820 A111290 A129140 * A196408 A091656 A273044
Adjacent sequences: A002577 A002578 A002579 * A002581 A002582 A002583


KEYWORD

nonn,easy,cons


AUTHOR

N. J. A. Sloane


STATUS

approved



