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A366164 Decimal expansion of the absolute value of the imaginary part of the larger pair of the 4 complex roots of x^4 + x^2 + x + 1 = 0. 2

%I #8 Oct 27 2023 11:52:56

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

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

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

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

%C The 4 roots are -(A366162) +- i*(A366163) and (A366162) +- i*D, where D is the constant given by this sequence.

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

%e 1.120873489937059302856055357373632173488591417333...

%o (PARI) vecmax (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)[4] \\ _Charles R Greathouse IV_, Oct 27 2023

%Y Cf. A366162, A366163.

%K nonn,cons

%O 1,3

%A _Hugo Pfoertner_, Oct 02 2023

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