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Plastic constant
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Where we used the cubic formula^{[2]} to solve with
giving the roots
where
Decimal expansion of the plastic constant
x 3 − x − 1 

{1, 3, 2, 4, 7, 1, 7, 9, 5, 7, 2, 4, 4, 7, 4, 6, 0, 2, 5, 9, 6, 0, 9, 0, 8, 8, 5, 4, 4, 7, 8, 0, 9, 7, 3, 4, 0, 7, 3, 4, 4, 0, 4, 0, 5, 6, 9, 0, 1, 7, 3, 3, 3, 6, 4, 5, 3, 4, ...}
Padovan sequence and Perrin sequence
The linear recurrence with constant coefficients of order3 
a0 = a1 = a2 = 1 
a0 = 3, a1 = 0, a2 = 2 
The limit ratio of the recurrence gives the plastic constant
Continued fraction and nested radicals expansions
The simple continued fraction expansion of the plastic constant is
x 3 = x + 1 

{1, 3, 12, 1, 1, 3, 2, 3, 2, 4, 2, 141, 80, 2, 5, 1, 2, 8, 2, 1, 1, 3, 1, 8, 2, 1, 1, 14, 1, 1, 2, 1, 1, 1, 3, 1, 10, 4, 40, 1, 1, 2, 4, 9, 1, 1, 3, 3, 3, 2, 1, 17, 7, 5, 1, 1, ...}
The plastic constant has the simplest nested cubic radicals expansion (the all one's sequence)
since
If we consider the simplest nested square radicals expansion, we get the Golden ratio instead.
See also
Notes
 ↑ Not to be confused with the silver ratio, i.e.
.1 + √ 2  ↑ Weisstein, Eric W., Cubic Formula, from MathWorld—A Wolfram Web Resource.
External links
 Weisstein, Eric W., Plastic Constant, from MathWorld—A Wolfram Web Resource.
 Weisstein, Eric W., Padovan Sequence, from MathWorld—A Wolfram Web Resource.
 Weisstein, Eric W., Perrin Sequence, from MathWorld—A Wolfram Web Resource.