A002581 - OEIS

%I M3220 N1304 #64 Feb 16 2025 08:32:26

%S 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,

%T 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,

%U 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

%N Decimal expansion of cube root of 3.

%C The largest k^(1/k), for any natural number k, occurs when k = 3 = A000227(1). - _Stanislav Sykora_, Jun 04 2014

%C 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

%C (1/3)*log(3) = -lim_{n->oo} (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

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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

%D 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.

%H Harry J. Smith, <a href="/A002581/b002581.txt">Table of n, a(n) for n = 1..20000</a>

%H Simon Plouffe, <a href="https://web.archive.org/web/20150911212405/http://www.worldwideschool.org/library/books/sci/math/MiscellaneousMathematicalConstants/chap15.html">The cube root of 3 to 2000 places</a>. [Wayback Machine link]

%H Simon Plouffe, <a href="http://www.plouffe.fr/simon/constants/cuberoot3.txt">The cube root of 3 to 2000 places</a>.

%H Harry Pollard, <a href="http://www.jstor.org/stable/2317957">Problem E 2190</a>, Elementary Problems, The American Mathematical Monthly, Vol. 76, No. 8 (1969), p. 937; <a href="http://www.jstor.org/stable/2316222">A Special Property of 3</a>, Solutions to Problem E 2190, by Douglas Lind and Charles Wexler, ibid., Vol. 77, No. 7 (1970), p. 768.

%H Horace S. Uhler, <a href="/A002580/a002580.pdf">Many-figure approximations for cubed root of 2, cubed root of 3, cubed root of 4, and cubed root of 9 with chi2 data</a>, Scripta Math. 18, (1952). 173-176. [Annotated scanned copies of pages 175 and 176 only]

%H Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/Landau-KolmogorovConstants.html">Landau-Kolmogorov Constants</a>.

%H <a href="/index/Al#algebraic_03">Index entries for algebraic numbers, degree 3</a>.

%F 3^(1/3) >= min(k^(1/m), m^(1/k)) for any positive integers k and m (Pollard, 1969). - _Amiram Eldar_, Feb 14 2025

%e 1.442249570307408382321638310780109588391869253499350577546416...

%t RealDigits[N[3^(1/3), 200]] (* _Vladimir Joseph Stephan Orlovsky_, May 27 2010 *)

%o (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

%Y Cf. A002946 (continued fraction).

%K nonn,cons,changed

%O 1,2

%A _N. J. A. Sloane_