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%I #14 Oct 27 2023 12:07:15
%S 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,
%T 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,
%U 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
%N The unique positive root of x^5 - 2*x^4 - x^2 - x - 1.
%C 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)
%H Jay Pantone, Vincent Vatter, <a href="http://arxiv.org/abs/1605.04289">Growth rates of permutation classes: categorization up to the uncountability threshold</a>, arXiv:1605.04289 [math.CO], (13-May-2016)
%H Vincent Vatter, <a href="http://arxiv.org/abs/1605.04297">Growth rates of permutation classes: from countable to uncountable</a>, arXiv:1605.04297 [math.CO], (13-May-2016)
%H <a href="/index/Al#algebraic_05">Index entries for algebraic numbers, degree 5</a>
%e 2.305223928729300566314701910933320828238...
%t RealDigits[Root[x^5 - 2x^4 - x^2 - x - 1, 1], 10, 105][[1]] (* _Jean-François Alcover_, Jul 23 2018 *)
%o (PARI) default(realprecision,110); real(polroots(x^5-2*x^4-x^2-x-1)[1])
%o (PARI) polrootsreal(x^5-2*x^4-x^2-x-1)[1] \\ _Charles R Greathouse IV_, Oct 27 2023
%K nonn,cons
%O 1,1
%A _Joerg Arndt_, May 16 2016
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