cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A005480 Decimal expansion of cube root of 4.

Original entry on oeis.org

1, 5, 8, 7, 4, 0, 1, 0, 5, 1, 9, 6, 8, 1, 9, 9, 4, 7, 4, 7, 5, 1, 7, 0, 5, 6, 3, 9, 2, 7, 2, 3, 0, 8, 2, 6, 0, 3, 9, 1, 4, 9, 3, 3, 2, 7, 8, 9, 9, 8, 5, 3, 0, 0, 9, 8, 0, 8, 2, 8, 5, 7, 6, 1, 8, 2, 5, 2, 1, 6, 5, 0, 5, 6, 2, 4, 2, 1, 9, 1, 7, 3, 2, 7, 3, 5, 4, 4, 2, 1, 3, 2, 6, 2, 2, 2, 0, 9, 5, 7, 0, 2, 2, 9, 3, 4, 7, 6
Offset: 1

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Author

N. J. A. Sloane; entry revised Apr 23 2006

Keywords

Comments

Let h = 4^(1/3). Then (h+1,0) is the x-intercept of the shortest segment from the x-axis through (1,2) to the y-axis; see A197008. - Clark Kimberling, Oct 10 2011
Let h = 4^(1/3). The relative maximum of xy(x+y)=1 is (-1/sqrt(h), h). - Clark Kimberling, Oct 05 2020

Examples

			1.587401051968199474751705639272308260391493327899853...
		

References

  • 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 cubed root of 2, cubed root of 3, cubed root of 4, and cubed root of 9 with chi2 data, Scripta Math. 18, (1952), p. 173-176.

Crossrefs

Cf. A002947 (continued fraction). - Harry J. Smith, May 07 2009
Cf. A002580 (cube root of 2).

Programs

  • Mathematica
    RealDigits[N[4^(1/3), 200]] (* Vladimir Joseph Stephan Orlovsky, May 27 2010 *)
  • PARI
    default(realprecision, 20080); x=4^(1/3); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b005480.txt", n, " ", d));  \\ Harry J. Smith, May 07 2009, with a correction made May 19 2009

Formula

Equals Product_{k>=0} (1 + (-1)^k/(3*k + 1)). - Amiram Eldar, Jul 25 2020
Equals A002580^2. - Michel Marcus, Jan 08 2022
Equals hypergeom([1/3, 1/6], [2/3], 1). - Peter Bala, Mar 02 2022