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. - Jean-François Alcover, Jul 17 2014
(1/3)*log(3) = -Lim_{n-> Infinity} (n-th derivative zeta(n+1)) / (n-1)-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, Many-figure 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), 173-176.
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, Many-figure 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). 173-176. [Annotated scanned copies of pages 175 and 176 only]
Eric Weisstein's MathWorld, Landau-Kolmogorov 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=(x-d)*10; write("b002581.txt", n, " ", d)); \\ Harry J. Smith, May 07 2009
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
STATUS
approved