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%I A139340 #25 Oct 27 2023 10:02:32
%S A139340 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 A139340 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 A139340 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 A139340 Decimal expansion of the cube root of the golden ratio. That is, the decimal expansion of ((1+sqrt(5))/2)^(1/3).
%C A139340 Larger of the real roots of x^6 - x^3 - 1. - _Charles R Greathouse IV_, Apr 14 2014
%H A139340 Chai Wah Wu, <a href="/A139340/b139340.txt">Table of n, a(n) for n = 1..10000</a>
%H A139340 <a href="/index/Al#algebraic_06">Index entries for algebraic numbers, degree 6</a>
%e A139340 1.1739849967053285...
%p A139340 phi := (sqrt(5)+1)/2 ; evalf(root[3](phi)) ; # _R. J. Mathar_, Oct 16 2015
%t A139340 RealDigits[N[GoldenRatio^(1/3),200]][[1]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 06 2012 *)
%o A139340 (PARI) polrootsreal(x^6-x^3-1)[2] \\ _Charles R Greathouse IV_, Apr 14 2014
%Y A139340 Cf. A001622, A094214, A104457, A098317, A002390, A139339.
%K A139340 nonn,cons
%O A139340 1,3
%A A139340 _Mohammad K. Azarian_, Apr 14 2008

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