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A316605 Decimal expansion of the fifth smallest known Salem number.

%I A316605 #10 Feb 16 2025 08:33:56
%S A316605 1,2,1,6,3,9,1,6,6,1,1,3,8,2,6,5,0,9,1,6,2,6,8,0,6,3,1,1,1,9,9,4,6,3,
%T A316605 3,2,7,7,2,2,2,5,3,6,0,6,5,7,0,5,7,0,7,5,7,5,6,0,4,2,7,0,6,5,8,3,8,3,
%U A316605 1,2,1,2,9,4,6,1,8,4,9,5,9,4,4,2,6,3,7,9,6,6,6,7,0,9,5,4,3,9,5,4,2,8
%N A316605 Decimal expansion of the fifth smallest known Salem number.
%H A316605 M. J. Mossinghoff, <a href="http://www.cecm.sfu.ca/~mjm/Lehmer/lists/SalemList.html">Small Salem Numbers</a>
%H A316605 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/SalemConstants.html">Salem Constants.</a>
%H A316605 Wikipedia, <a href="http://en.wikipedia.org/wiki/Salem_number">Salem number</a>
%H A316605 <a href="/index/Al#algebraic_10">Index entries for algebraic numbers, degree 10</a>.
%F A316605 p = 1 - x^4 - x^5 - x^6 + x^10.
%e A316605 1.21639166113826509162680631119946332772225360657057075756042706583831...
%t A316605 c1 = {1, 0, 0, 0, -1, -1};
%t A316605 c2 = Join[c1, Reverse[Most[c1]]];
%t A316605 p = (x^Range[0, Length[c2] - 1]).c2;
%t A316605 sigma5 = Root[p, x, 2];
%t A316605 RealDigits[sigma5, 10, 102][[1]]
%o A316605 (PARI) polrootsreal(1 - x^4 - x^5 - x^6 + x^10)[2] \\ _Charles R Greathouse IV_, Feb 11 2025
%Y A316605 Cf. A073011 (sigma1), A219300 (sigma2), A306078 (sigma3), A306079 (sigma4), A316606 (sigma6), A316607 (sigma7), A316608 (sigma8), A316609 (sigma9), A316610 (sigma10).
%K A316605 nonn,cons
%O A316605 1,2
%A A316605 _Jean-François Alcover_, Jul 08 2018