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A316606 Decimal expansion of the sixth smallest known Salem number.

%I A316606 #13 Feb 16 2025 08:33:56
%S A316606 1,2,1,9,7,2,0,8,5,9,0,4,0,3,1,1,8,4,4,1,6,9,6,0,6,7,6,0,4,1,4,6,7,7,
%T A316606 9,4,4,3,9,0,4,1,5,5,0,5,5,4,1,5,6,9,6,7,8,2,8,7,9,7,4,4,1,7,8,7,3,3,
%U A316606 8,4,6,4,5,9,9,0,8,3,9,0,6,5,8,3,5,5,3,9,3,2,0,7,8,5,1,6,2,5,9,5,7,8
%N A316606 Decimal expansion of the sixth smallest known Salem number.
%H A316606 M. J. Mossinghoff, <a href="http://www.cecm.sfu.ca/~mjm/Lehmer/lists/SalemList.html">Small Salem Numbers</a>
%H A316606 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/SalemConstants.html">Salem Constants.</a>
%H A316606 Wikipedia, <a href="http://en.wikipedia.org/wiki/Salem_number">Salem number</a>
%H A316606 <a href="/index/Al#algebraic_18">Index entries for algebraic numbers, degree 18</a>.
%F A316606 Equals root of p = 1 - x - x^8 + x^9 - x^10 - x^17 + x^18 with largest absolute value.
%e A316606 1.219720859040311844169606760414677944390415505541569678287974417873...
%t A316606 c1 = {1, -1, 0, 0, 0, 0, 0, 0, -1, 1};
%t A316606 c2 = Join[c1, Reverse[Most[c1]]];
%t A316606 p = (x^Range[0, Length[c2] - 1]).c2;
%t A316606 sigma6 = Root[p, x, 2];
%t A316606 RealDigits[sigma6, 10, 102][[1]]
%o A316606 (PARI) polrootsreal(1 - x - x^8 + x^9 - x^10 - x^17 + x^18)[2] \\ _Charles R Greathouse IV_, Feb 11 2025
%Y A316606 Cf. A073011 (sigma1), A219300 (sigma2), A306078 (sigma3 ), A306079 (sigma4), A316605 (sigma5), A316607 (sigma7), A316608 (sigma8), A316609 (sigma9), A316610 (sigma10).
%K A316606 nonn,cons
%O A316606 1,2
%A A316606 _Jean-François Alcover_, Jul 08 2018