A139340 Decimal expansion of the cube root of the golden ratio. That is, the decimal expansion of ((1+sqrt(5))/2)^(1/3).

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, 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, 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

Offset: 1

Author

Mohammad K. Azarian, Apr 14 2008

Keywords

• nonn
• cons

Comments

Larger of the real roots of x^6 - x^3 - 1. - Charles R Greathouse IV, Apr 14 2014

Examples

			1.1739849967053285...
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000
• Index entries for algebraic numbers, degree 6

Crossrefs

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

Programs

Maple

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

Mathematica

RealDigits[N[GoldenRatio^(1/3),200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Feb 06 2012 *)

PARI

polrootsreal(x^6-x^3-1)[2] \\ Charles R Greathouse IV, Apr 14 2014