A366162 Decimal expansion of the absolute value of the real part of the 4 complex roots of x^4 + x^2 + x + 1 = 0.

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

Offset

0,1

Comments

The 4 roots are -R +- i*(A366163) and R +- i*(A366164), where R is the constant given by this sequence.

Links

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

Jose Capco and Claus Scheiderer, Expository notes on sum of square of polynomials with rational coefficients, Research Institute for Symbolic Computation, Johannes Kepler Universitaet Linz, Technical report, 2019 (see Example 1, page 3).

Index entries for algebraic numbers, degree 6

Example

0.547423794586058597522831865993036666857208161949756527904813189143588759...

Mathematica

RealDigits[Abs[Re[N[Root[x^4+x^2+x+1, 1], 120]]]][[1]] (* Harvey P. Dale, Nov 28 2023 *)

Prog

(PARI) abs (real (polroots (x^4 + x^2 + x + 1)[1]))
(PARI) polrootsreal(64*x^6 + 32*x^4 - 12*x^2 - 1)[2] \\ Charles R Greathouse IV, Oct 27 2023

Crossrefs

Cf. A366163, A366164.

Sequence in context: A177161 A154776 A188932 * A372954 A195428 A254373

Adjacent sequences: A366159 A366160 A366161 * A366163 A366164 A366165

Keyword

nonn,cons

Author

Hugo Pfoertner, Oct 02 2023

Status

approved