

A002581


Decimal expansion of cube root of 3.
(Formerly M3220 N1304)


20



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

1,2


COMMENTS

The largest k^(1/k), for any natural number k, occurs when k = 3 = A000227(1).  Stanislav Sykora, Jun 04 2014
3^(1/3) is also the Kolmogorov constant C(3,2) in the case supremum norm on the real line.  JeanFrançois Alcover, Jul 17 2014
(1/3)*log(3) = Lim_{n> Infinity} (nth derivative zeta(n+1)) / (n1)th derivative zeta(n)) = 0.3662040962227... Convergence is to 25 digits by n = ~1000. zeta is the Riemann zeta function.  Richard R. Forberg, Feb 24 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 cube root of 2, cube root of 3, cube root of 4 and cube root of 9 with chi_2 data, Scripta Math. 18, (1952), 173176.


LINKS

Harry J. Smith, Table of n, a(n) for n = 1..20000
Simon Plouffe, The cube root of 3 to 2000 places
Simon Plouffe, The cube root of 3 to 2000 places
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 MathWorld, LandauKolmogorov Constants


EXAMPLE

1.442249570307408382321638310780109588391869253499350577546416...


MATHEMATICA

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


PROG

(PARI) { default(realprecision, 20080); x=3^(1/3); for (n=1, 20000, d=floor(x); x=(xd)*10; write("b002581.txt", n, " ", d)); } \\ Harry J. Smith, May 07 2009


CROSSREFS

Cf. A002946 = Continued fraction.  Harry J. Smith, May 07 2009
Sequence in context: A162232 A029676 A105190 * A161778 A099655 A276149
Adjacent sequences: A002578 A002579 A002580 * A002582 A002583 A002584


KEYWORD

nonn,cons


AUTHOR

N. J. A. Sloane, Apr 30 1991


STATUS

approved



