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A366162 Decimal expansion of the absolute value of the real part of the 4 complex roots of x^4 + x^2 + x + 1 = 0. 2
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 (list; constant; graph; refs; listen; history; text; internal format)
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
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).
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
Sequence in context: A177161 A154776 A188932 * A195428 A254373 A343564
KEYWORD
nonn,cons
AUTHOR
Hugo Pfoertner, Oct 02 2023
STATUS
approved

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Last modified April 18 10:39 EDT 2024. Contains 371779 sequences. (Running on oeis4.)