|
|
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
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
FORMULA
|
|
|
EXAMPLE
|
1.13715804260325761283766795192009876258136039422990658596288796494425...
|
|
MATHEMATICA
|
N[Reduce[2+6d-6d^3==0, d], 100]
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|