The On-Line Encyclopedia of Integer Sequences (OEIS)

A210463 revision #17

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

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OFFSET

0,1

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

LINKS

Table of n, a(n) for n=0..124.

FORMULA

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

EXAMPLE

0.744861766619744236593170428604392367240163...

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 *)

PROG

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

CROSSREFS

Cf. A075778, A210462.

Sequence in context: A316161 A377010 A153349 * A154172 A021577 A019810

Adjacent sequences: A210460 A210461 A210462 * A210464 A210465 A210466

KEYWORD

cons,easy,nonn

AUTHOR

R. J. Mathar, Jan 22 2013

STATUS

approved