A005480 Decimal expansion of cube root of 4. (Formerly M3771)

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

1,2

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

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.

Links

Harry J. Smith, Table of n, a(n) for n = 1..20000

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]

Index entries for algebraic numbers, degree 3

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

Example

1.587401051968199474751705639272308260391493327899853...

Mathematica

RealDigits[N[4^(1/3), 200]] (* Vladimir Joseph Stephan Orlovsky, May 27 2010 *)

Prog

(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

Crossrefs

Cf. A002947 (continued fraction). - Harry J. Smith, May 07 2009

Cf. A002580 (cube root of 2).

Sequence in context: A133731 A021067 A047914 * A204921 A021867 A346192

Adjacent sequences: A005477 A005478 A005479 * A005481 A005482 A005483

Keyword

nonn,cons,easy

Author

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

Status

approved