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A139340 Decimal expansion of the cube root of the golden ratio. That is, the decimal expansion of ((1+sqrt(5))/2)^(1/3). 14
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

REFERENCES

Mohammad K. Azarian, Problem 123, Missouri Journal of Mathematical Sciences, Vol. 10, No. 3, Fall 1998, p. 176.  Solution published in Vol. 12, No. 1, Winter 2000, pp. 61-62.

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10000

EXAMPLE

1.1739849967053285...

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 *)

PROG

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

CROSSREFS

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

Sequence in context: A021579 A139788 A093525 * A195725 A105168 A134883

Adjacent sequences:  A139337 A139338 A139339 * A139341 A139342 A139343

KEYWORD

nonn,cons

AUTHOR

Mohammad K. Azarian, Apr 14 2008

STATUS

approved

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Last modified April 23 15:38 EDT 2017. Contains 285329 sequences.