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.

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, 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, 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

Offset

0,1

Comments

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

Links

Table of n, a(n) for n=0..95.

Index entries for algebraic numbers, degree 12

Example

0.58565197968957261459032861223356319799409789265437719426362121839705...

Mathematica

First[RealDigits[Im[Root[#^4 + #^2 + # + 1 &, 1]], 10, 100]] (* Paolo Xausa, Jun 25 2024 *)

Prog

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

Crossrefs

Cf. A366162, A366164.

Sequence in context: A306204 A178331 A199395 * A371945 A358630 A100610

Adjacent sequences: A366160 A366161 A366162 * A366164 A366165 A366166

Keyword

nonn,cons

Author

Hugo Pfoertner, Oct 02 2023

Status

approved