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A273066 Decimal expansion of the real root of x^3 - 2x + 2, negated. 3
1, 7, 6, 9, 2, 9, 2, 3, 5, 4, 2, 3, 8, 6, 3, 1, 4, 1, 5, 2, 4, 0, 4, 0, 9, 4, 6, 4, 3, 3, 5, 0, 3, 3, 4, 9, 2, 6, 7, 0, 5, 5, 3, 0, 4, 5, 8, 9, 8, 8, 5, 7, 0, 0, 4, 2, 3, 3, 1, 0, 6, 1, 3, 0, 4, 0, 2, 6, 7, 3, 8, 1, 7, 3, 5, 0, 6, 6, 8, 3, 2, 9, 0, 6, 8, 7, 4, 1, 2, 2, 1, 4, 9, 4, 4, 5, 4, 8, 1, 8, 1, 2, 7, 1, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The roots of x^3 + A273065*x^2 - A273066*x + A273067 are A273065, -A273066, and A273067. The only other real, cubic, monic polynomial with nonzero constant term and equal coefficients and roots when ignoring the leading coefficient is x^3 + x^2 - x - 1 (per the Math Overflow link).

LINKS

Table of n, a(n) for n=1..105.

A. J. Di Scala and O. Macia, Finiteness of Ulam Polynomials, arXiv:0904.0133 [math.AG], 2009.

R. Stanley, R. Israel et al., Math Overflow: Which polynomial's roots are its coefficients?, Sep 3 2015.

P. R. Stein, On Polynomial Equations with Coefficients Equal to Their Roots, The American Mathematical Monthly, Vol. 73, No. 3 (Mar., 1966), pp. 272-274.

FORMULA

((9-sqrt(57))^(1/3))/(3^(2/3)) + 2/((3(9-sqrt(57)))^(1/3)) (from Wolfram Alpha).

EXAMPLE

1.7692923542386314152404094643350334926705530458988570042331061304026738...

PROG

(PARI) default(realprecision, 200);

-solve(x = -1.8, -1.7, x^3 - 2*x + 2)

CROSSREFS

Cf. A273065, A273067.

Sequence in context: A198605 A021017 A219705 * A257964 A178816 A200106

Adjacent sequences:  A273063 A273064 A273065 * A273067 A273068 A273069

KEYWORD

nonn,cons

AUTHOR

Rick L. Shepherd, May 14 2016

STATUS

approved

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Last modified April 6 22:23 EDT 2020. Contains 333291 sequences. (Running on oeis4.)