A210463 Decimal expansion of the absolute value of the imaginary part of the two complex roots of x^3-x^2+1.

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

Offset: 0

Author

R. J. Mathar, Jan 22 2013

Keywords

• cons
• easy
• nonn

Comments

An algebraic number of degree 6. - Charles R Greathouse IV, Apr 14 2014

The denominator of this algebraic number is 2, since its double is an algebraic integer. - Charles R Greathouse IV, Nov 12 2014

Examples

			0.744861766619744236593170428604392367240163...
		

Links

• Index entries for algebraic numbers, degree 6

Crossrefs

Cf. A075778, A210462.

Programs

Maple

A075778neg := proc()
        1/3-root[3](25/2-3*sqrt(69)/2)/3 -root[3](25/2+3*sqrt(69)/2)/3;
end proc:
A210463 := proc()
        local a075778,a210462 ;
        a075778 := A075778neg() ;
        a210462 := A210462() ;
        -1/a075778-a210462^2 ;
        sqrt(%) ;
end proc:
evalf(A210463()) ;

Mathematica

-((2^(1/3)*(25 - 3*Sqrt[69])^(2/3) - 2)/(2*2^(2/3)*Sqrt[3]*(25 - 3*Sqrt[69])^(1/3))) // RealDigits[#, 10, 125]& // First (* Jean-François Alcover, Feb 20 2013 *)

PARI

polrootsreal(64*x^6+32*x^4+4*x^2-23)[2] \\ Charles R Greathouse IV, Apr 14 2014

Formula

Equals sqrt(1/A075778-A210462^2).