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A316608 Decimal expansion of the eighth smallest known Salem number.

%I A316608 #7 Feb 16 2025 08:33:56
%S A316608 1,2,3,2,6,1,3,5,4,8,5,9,3,1,2,1,0,0,3,9,6,2,7,3,1,6,9,4,8,0,7,9,0,9,
%T A316608 7,9,1,4,1,1,5,7,7,3,7,1,2,0,9,8,3,1,0,4,6,7,2,9,9,1,6,5,8,2,0,5,3,8,
%U A316608 3,9,3,5,1,3,7,3,8,9,5,7,0,3,1,3,4,9,7,8,4,8,8,5,3,0,3,2,4,9,2,2,3,3
%N A316608 Decimal expansion of the eighth smallest known Salem number.
%H A316608 M. J. Mossinghoff, <a href="http://www.cecm.sfu.ca/~mjm/Lehmer/lists/SalemList.html">Small Salem Numbers</a>
%H A316608 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/SalemConstants.html">Salem Constants.</a>
%H A316608 Wikipedia, <a href="http://en.wikipedia.org/wiki/Salem_number">Salem number</a>
%H A316608 <a href="/index/Al#algebraic_20">Index entries for algebraic numbers, degree 20</a>.
%F A316608 p = 1 - x - x^5 + x^6 - x^9 + x^10 - x^11 + x^14 - x^15 - x^19 + x^20.
%e A316608 1.2326135485931210039627316948079097914115773712098310467299165820538...
%t A316608 c1 = {1, -1, 0, 0, 0, -1, 1, 0, 0, -1, 1};
%t A316608 c2 = Join[c1, Reverse[Most[c1]]];
%t A316608 p = (x^Range[0, Length[c2] - 1]).c2;
%t A316608 sigma8 = Root[p, x, 2];
%t A316608 RealDigits[sigma8, 10, 102][[1]]
%o A316608 (PARI) polrootsreal(1 - x - x^5 + x^6 - x^9 + x^10 - x^11 + x^14 - x^15 - x^19 + x^20)[2] \\ _Charles R Greathouse IV_, Feb 11 2025
%Y A316608 Cf. A073011 (sigma1), A219300 (sigma2), A306078 (sigma3 ), A306079 (sigma4), A316605 (sigma5), A316606 (sigma6), A316607 (sigma7), A316609 (sigma9), A316610 (sigma10).
%K A316608 nonn,cons
%O A316608 1,2
%A A316608 _Jean-François Alcover_, Jul 08 2018