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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 (list; constant; graph; refs; listen; history; text; internal format)
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 |a|s^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

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Last modified January 25 19:09 EST 2020. Contains 331249 sequences. (Running on oeis4.)