A272591 The unique positive root of x^5 - 2*x^4 - x^2 - x - 1.

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

Offset

1,1

Comments

Theorem 9.7 from the Vatter reference: "There are only countably many growth rates of permutation classes below X but uncountably many growth rates in every open neighborhood of it. Moreover, every growth rate of permutation classes below X is achieved by a sum closed permutation class." (where X is the constant we are looking at)

Links

Table of n, a(n) for n=1..105.

Jay Pantone, Vincent Vatter, Growth rates of permutation classes: categorization up to the uncountability threshold, arXiv:1605.04289 [math.CO], (13-May-2016)

Vincent Vatter, Growth rates of permutation classes: from countable to uncountable, arXiv:1605.04297 [math.CO], (13-May-2016)

Index entries for algebraic numbers, degree 5

Example

2.305223928729300566314701910933320828238...

Mathematica

RealDigits[Root[x^5 - 2x^4 - x^2 - x - 1, 1], 10, 105][[1]] (* Jean-François Alcover, Jul 23 2018 *)

Prog

(PARI) default(realprecision, 110); real(polroots(x^5-2*x^4-x^2-x-1)[1])
(PARI) polrootsreal(x^5-2*x^4-x^2-x-1)[1] \\ Charles R Greathouse IV, Oct 27 2023

Crossrefs

Sequence in context: A071322 A072594 A353051 * A339694 A074722 A370744

Adjacent sequences: A272588 A272589 A272590 * A272592 A272593 A272594

Keyword

nonn,cons

Author

Joerg Arndt, May 16 2016

Status

approved