

A212886


Decimal expansion of 2/(3*sqrt(3)) = 2*sqrt(3)/9.


0



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

0,1


COMMENTS

Consider any cubic polynomial f(x) = a(x  r)(x  (r + s))(x (r + 2s)), where a, r, and s are real numbers with s > 0 and nonzero a; i.e., any cubic polynomial with three distinct real roots, of which the middle root, r + s, is equidistant (with distance s) from the other two. Then the absolute value of f's local extrema is as^3*(2sqrt(3)/9). They occur at x = r + s + s*(sqrt(3)/3), with the local maximum, M, at r + s  s*sqrt(3)/3 when a is positive and at r + s + s*sqrt(3)/3 when a is negative (and the local minimum, m, vice versa). Of course m = M < 0.
A quadratic number with denominator 9 and minimal polynomial 27x^2  4.  Charles R Greathouse IV, Apr 21 2016


LINKS

Table of n, a(n) for n=0..104.


FORMULA

2/9*sqrt(3) = 2/9*A002194.


EXAMPLE

0.384900179459750509672765853667971637098401167513417917345734...


MATHEMATICA

RealDigits[2/(3*Sqrt[3]), 10, 105] (* T. D. Noe, May 31 2012 *)


PROG

(PARI) default(realprecision, 1000); 2*sqrt(3)/9


CROSSREFS

Cf. A002194, A020760.
Sequence in context: A240242 A010628 A225456 * A127438 A303217 A106292
Adjacent sequences: A212883 A212884 A212885 * A212887 A212888 A212889


KEYWORD

nonn,cons


AUTHOR

Rick L. Shepherd, May 29 2012


STATUS

approved



