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A316609 Decimal expansion of the ninth smallest known Salem number.

%I A316609 #9 Feb 16 2025 08:33:56
%S A316609 1,2,3,5,6,6,4,5,8,0,3,8,9,7,4,7,3,0,8,1,0,5,1,6,9,3,5,1,5,3,1,2,6,3,
%T A316609 4,7,9,7,2,3,5,1,0,0,4,2,7,4,6,2,3,9,0,7,7,6,5,0,4,3,8,0,7,7,2,0,6,3,
%U A316609 1,1,9,2,4,9,4,0,2,7,8,1,4,9,8,8,9,1,6,6,0,7,4,0,4,2,6,3,8,5,9,2,5
%N A316609 Decimal expansion of the ninth smallest known Salem number.
%H A316609 M. J. Mossinghoff, <a href="http://www.cecm.sfu.ca/~mjm/Lehmer/lists/SalemList.html">Small Salem Numbers</a>
%H A316609 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/SalemConstants.html">Salem Constants.</a>
%H A316609 Wikipedia, <a href="http://en.wikipedia.org/wiki/Salem_number">Salem number</a>
%H A316609 <a href="/index/Al#algebraic_22">Index entries for algebraic numbers, degree 22</a>.
%F A316609 p = 1 - x^2 - x^3 + x^7 + x^8 - x^10 - x^11 - x^12 + x^14 + x^15 - x^19 - x^20 + x^22.
%e A316609 1.2356645803897473081051693515312634797235100427462390776504380772063...
%t A316609 c1 = {1, 0, -1, -1, 0, 0, 0, 1, 1, 0, -1, -1};
%t A316609 c2 = Join[c1, Reverse[Most[c1]]];
%t A316609 p = (x^Range[0, Length[c2] - 1]).c2;
%t A316609 sigma9 = Root[p, x, 2];
%t A316609 RealDigits[sigma9, 10, 101][[1]]
%o A316609 (PARI) polrootsreal(1 - x^2 - x^3 + x^7 + x^8 - x^10 - x^11 - x^12 + x^14 + x^15 - x^19 - x^20 + x^22)[2] \\ _Charles R Greathouse IV_, Feb 11 2025
%Y A316609 Cf. A073011 (sigma1), A219300 (sigma2), A306078 (sigma3 ), A306079 (sigma4), A316605 (sigma5), A316606 (sigma6), A316607 (sigma7), A316608 (sigma8), A316610 (sigma10).
%K A316609 nonn,cons
%O A316609 1,2
%A A316609 _Jean-François Alcover_, Jul 08 2018