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Decimal expansion of the cube root of the golden ratio. That is, the decimal expansion of ((1+sqrt(5))/2)^(1/3).
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%I #25 Oct 27 2023 10:02:32

%S 1,1,7,3,9,8,4,9,9,6,7,0,5,3,2,8,5,0,9,9,6,6,6,8,3,9,7,1,8,8,6,2,6,6,

%T 7,4,1,9,5,5,7,9,9,0,6,9,0,9,0,8,1,1,2,0,6,7,7,6,0,5,0,0,3,3,0,6,8,2,

%U 7,9,9,0,3,1,0,4,8,2,0,2,7,7,8,1,8,4,0,6,5,7,4,7,5,8,1,1,4,3,9,9,9,2,7,7,3

%N Decimal expansion of the cube root of the golden ratio. That is, the decimal expansion of ((1+sqrt(5))/2)^(1/3).

%C Larger of the real roots of x^6 - x^3 - 1. - _Charles R Greathouse IV_, Apr 14 2014

%H Chai Wah Wu, <a href="/A139340/b139340.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Al#algebraic_06">Index entries for algebraic numbers, degree 6</a>

%e 1.1739849967053285...

%p phi := (sqrt(5)+1)/2 ; evalf(root[3](phi)) ; # _R. J. Mathar_, Oct 16 2015

%t RealDigits[N[GoldenRatio^(1/3),200]][[1]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 06 2012 *)

%o (PARI) polrootsreal(x^6-x^3-1)[2] \\ _Charles R Greathouse IV_, Apr 14 2014

%Y Cf. A001622, A094214, A104457, A098317, A002390, A139339.

%K nonn,cons

%O 1,3

%A _Mohammad K. Azarian_, Apr 14 2008