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A316607 Decimal expansion of the seventh smallest known Salem number.

%I A316607 #7 Feb 16 2025 08:33:56
%S A316607 1,2,3,0,3,9,1,4,3,4,4,0,7,2,2,4,7,0,2,7,9,0,1,7,7,9,3,8,9,7,5,2,7,9,
%T A316607 0,1,7,5,6,6,5,7,4,4,8,9,6,6,1,7,5,6,2,4,1,4,0,1,9,1,4,2,3,6,1,7,2,8,
%U A316607 1,3,4,4,7,8,5,3,5,4,5,4,1,6,7,3,5,9,8,4,6,5,1,6,6,2,4,0,8,5,2,8,5,6
%N A316607 Decimal expansion of the seventh smallest known Salem number.
%H A316607 M. J. Mossinghoff, <a href="http://www.cecm.sfu.ca/~mjm/Lehmer/lists/SalemList.html">Small Salem Numbers</a>
%H A316607 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/SalemConstants.html">Salem Constants.</a>
%H A316607 Wikipedia, <a href="http://en.wikipedia.org/wiki/Salem_number">Salem number</a>
%H A316607 <a href="/index/Al#algebraic_10">Index entries for algebraic numbers, degree 10</a>.
%F A316607 p = 1 - x^3 - x^5 - x^7 + x^10.
%e A316607 1.2303914344072247027901779389752790175665744896617562414019142361728...
%t A316607 c1 = {1, 0, 0, -1, 0, -1};
%t A316607 c2 = Join[c1, Reverse[Most[c1]]];
%t A316607 p = (x^Range[0, Length[c2] - 1]).c2;
%t A316607 sigma7 = Root[p, x, 2];
%t A316607 RealDigits[sigma7, 10, 102][[1]]
%o A316607 (PARI) polrootsreal(1 - x^3 - x^5 - x^7 + x^10)[2] \\ _Charles R Greathouse IV_, Feb 11 2025
%Y A316607 Cf. A073011 (sigma1), A219300 (sigma2), A306078 (sigma3 ), A306079 (sigma4), A316605 (sigma5), A316606 (sigma6), A316608 (sigma8), A316609 (sigma9), A316610 (sigma10).
%K A316607 nonn,cons
%O A316607 1,2
%A A316607 _Jean-François Alcover_, Jul 08 2018