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%I M3771 #60 Aug 21 2023 10:11:26
%S 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,
%T 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,
%U 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
%N Decimal expansion of cube root of 4.
%C 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
%C Let h = 4^(1/3). The relative maximum of xy(x+y)=1 is (-1/sqrt(h), h). - _Clark Kimberling_, Oct 05 2020
%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 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.
%H Harry J. Smith, <a href="/A005480/b005480.txt">Table of n, a(n) for n = 1..20000</a>
%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 <a href="/index/Al#algebraic_03">Index entries for algebraic numbers, degree 3</a>
%F Equals Product_{k>=0} (1 + (-1)^k/(3*k + 1)). - _Amiram Eldar_, Jul 25 2020
%F Equals A002580^2. - _Michel Marcus_, Jan 08 2022
%F Equals hypergeom([1/3, 1/6], [2/3], 1). - _Peter Bala_, Mar 02 2022
%e 1.587401051968199474751705639272308260391493327899853...
%t RealDigits[N[4^(1/3), 200]] (* _Vladimir Joseph Stephan Orlovsky_, May 27 2010 *)
%o (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
%Y Cf. A002947 (continued fraction). - _Harry J. Smith_, May 07 2009
%Y Cf. A002580 (cube root of 2).
%K nonn,cons,easy
%O 1,2
%A _N. J. A. Sloane_; entry revised Apr 23 2006
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