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A366163 Decimal expansion of the absolute value of the imaginary part of the smaller pair of the 4 complex roots of x^4 + x^2 + x + 1 = 0. 2

%I #7 Oct 27 2023 11:25:48

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

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

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

%N Decimal expansion of the absolute value of the imaginary part of the smaller pair of the 4 complex roots of x^4 + x^2 + x + 1 = 0.

%C The 4 roots are -(A366162) +- i*C and (A366162) +- i*(A366164), where C is the constant given by this sequence.

%H <a href="/index/Al#algebraic_12">Index entries for algebraic numbers, degree 12</a>

%e 0.58565197968957261459032861223356319799409789265437719426362121839705...

%o (PARI) vecmin (abs (imag (polroots (x^4 + x^2 + x + 1))))

%o (PARI) polrootsreal(4096*x^12 - 8192*x^10 + 7680*x^8 - 4480*x^6 - 368*x^4 - 312*x^2 + 257)[3] \\ _Charles R Greathouse IV_, Oct 27 2023

%Y Cf. A366162, A366164.

%K nonn,cons

%O 0,1

%A _Hugo Pfoertner_, Oct 02 2023

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Last modified April 24 00:30 EDT 2024. Contains 371917 sequences. (Running on oeis4.)