

A199589


Decimal expansion of the greatest root of 6x^3  6x  2 = 0.


2



1, 1, 3, 7, 1, 5, 8, 0, 4, 2, 6, 0, 3, 2, 5, 7, 6, 1, 2, 8, 3, 7, 6, 6, 7, 9, 5, 1, 9, 2, 0, 0, 9, 8, 7, 6, 2, 5, 8, 1, 3, 6, 0, 3, 9, 4, 2, 2, 9, 9, 0, 6, 5, 8, 5, 9, 6, 2, 8, 8, 7, 9, 6, 4, 9, 4, 4, 2, 5, 1, 0, 6, 6, 5, 6, 8, 5, 0, 9, 4, 5, 4, 9, 8, 5, 3, 1, 6, 7, 7, 7, 6, 7, 8, 9, 9, 7, 7, 0
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OFFSET

1,3


COMMENTS

If the side lengths of a quadrilateral form a harmonic progression in the ratio 1 : 1/(1+d) : 1/(1+2d) : 1/(1+3d) where d is the common difference between the denominators of the harmonic progression, then the triangle inequality condition requires that d be in the range f < d < g, where g = 1.1371580... and is the greatest root of the equation: 2 + 6d  6d^3 = 0. The value of f is given in A199590.


LINKS

Table of n, a(n) for n=1..99.


FORMULA

sqrt(4/3)*cos(Pi/18).  Charles R Greathouse IV, Nov 10 2011


EXAMPLE

1.13715804260325761283766795192009876258136039422990658596288796494425...


MATHEMATICA

N[Reduce[2+6d6d^3==0, d], 100]


PROG

(PARI) real(polroots(6*x^36*x2)[3]) \\ Charles R Greathouse IV, Nov 10 2011
(PARI) polrootsreal(6*x^36*x2)[3] \\ Charles R Greathouse IV, Apr 14 2014


CROSSREFS

Cf. A010503, A199220, A199221, A199590.
Sequence in context: A071792 A010781 A019806 * A080172 A133065 A335815
Adjacent sequences: A199586 A199587 A199588 * A199590 A199591 A199592


KEYWORD

nonn,cons


AUTHOR

Frank M Jackson, Nov 08 2011


STATUS

approved



