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A306079 Decimal expansion of the fourth smallest known Salem number.

%I A306079 #7 Feb 16 2025 08:33:54
%S A306079 1,2,0,2,6,1,6,7,4,3,6,8,8,6,0,4,2,6,1,1,1,8,2,9,5,4,1,5,9,4,8,6,1,9,
%T A306079 0,4,5,3,4,3,9,4,9,8,3,4,9,6,9,5,2,3,0,4,3,6,8,5,3,0,9,5,7,6,7,2,6,4,
%U A306079 5,4,0,6,5,8,7,6,3,6,5,5,5,3,7,7,2,6,7,1,0,8,0,0,5,5,1,8,2,6,5,7,6,7
%N A306079 Decimal expansion of the fourth smallest known Salem number.
%H A306079 M. J. Mossinghoff, <a href="http://www.cecm.sfu.ca/~mjm/Lehmer/lists/SalemList.html">Small Salem Numbers</a>
%H A306079 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/SalemConstants.html">Salem Constants.</a>
%H A306079 Wikipedia, <a href="http://en.wikipedia.org/wiki/Salem_number">Salem number</a>
%H A306079 <a href="/index/Al#algebraic_14">Index entries for algebraic numbers, degree 14</a>.
%e A306079 1.20261674368860426111829541594861904534394983496952304368530957672645...
%t A306079 c1 = {1, 0, -1, 0, 0, 0, 0, -1};
%t A306079 c2 = Join[c1, Reverse[Most[c1]]];
%t A306079 p = (x^Range[0, Length[c2]-1]).c2;
%t A306079 sigma4 = Root[p, x, 2];
%t A306079 RealDigits[sigma4, 10, 102][[1]]
%o A306079 (PARI) polrootsreal(x^14 - x^12 - x^7 - x^2 + 1)[2] \\ _Charles R Greathouse IV_, Feb 11 2025
%Y A306079 Cf. A073011 (sigma1), A219300 (sigma2), A306078 (sigma3).
%K A306079 nonn,cons
%O A306079 1,2
%A A306079 _Jean-François Alcover_, Jun 19 2018