

A199590


Decimal expansion (unsigned) of the greatest root of 6x^3 + 18x^2 + 12x + 2 = 0.


2



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

0,1


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 f = 0.257772801... and is the greatest root of the equation: 2 + 12d + 18d^2 + 6d^3 = 0. The value of g is given in A199589.


LINKS



FORMULA



EXAMPLE

0.257772801031440844729449397270635822708944125700977319782314639395808...


MATHEMATICA

N[Reduce[2+12d+18d^2+6d^3==0, d], 100]


PROG



CROSSREFS



KEYWORD



AUTHOR



EXTENSIONS



STATUS

approved



