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]
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
KEYWORD
AUTHOR
N. J. A. Sloane; entry revised Apr 23 2006
STATUS
approved