A002581 Decimal expansion of cube root of 3.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• cons

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->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

Examples

			1.442249570307408382321638310780109588391869253499350577546416...
		

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. [Wayback Machine link]
• Simon Plouffe, The cube root of 3 to 2000 places.
• Harry Pollard, Problem E 2190, Elementary Problems, The American Mathematical Monthly, Vol. 76, No. 8 (1969), p. 937; A Special Property of 3, Solutions to Problem E 2190, by Douglas Lind and Charles Wexler, ibid., Vol. 77, No. 7 (1970), p. 768.
• Horace 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.
• Index entries for algebraic numbers, degree 3.

Crossrefs

Cf. A002946 (continued fraction).

Programs

Mathematica

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

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

Formula

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