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Decimal expansion of the tenth smallest known Salem number.
5

%I #4 Jul 08 2018 21:30:41

%S 1,2,3,6,3,1,7,9,3,1,8,0,3,2,3,0,4,8,9,8,9,9,0,9,4,8,6,9,8,0,2,0,5,4,

%T 5,5,3,9,4,4,8,1,9,2,0,8,3,6,7,8,6,9,5,6,3,7,9,4,7,5,3,7,8,4,1,1,1,8,

%U 3,6,9,9,9,5,6,7,1,4,1,5,6,3,4,2,7,2,4,3,8,5,4,3,6,5,4,0,5,5,6,1,8,8

%N Decimal expansion of the tenth smallest known Salem number.

%H M. J. Mossinghoff, <a href="http://www.cecm.sfu.ca/~mjm/Lehmer/lists/SalemList.html">Small Salem Numbers</a>

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/SalemConstants.html">Salem Constants.</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Salem_number">Salem number</a>

%F p = 1 - x - x^8 - x^15 + x^16.

%e 1.2363179318032304898990948698020545539448192083678695637947537841118...

%t c1 = {1, -1, 0, 0, 0, 0, 0, 0, -1};

%t c2 = Join[c1, Reverse[Most[c1]]];

%t p = (x^Range[0, Length[c2] - 1]).c2;

%t sigma10 = Root[p, x, 2];

%t RealDigits[sigma10, 10, 102][[1]]

%Y Cf. A073011 (sigma1), A219300 (sigma2), A306078 (sigma3 ), A306079 (sigma4), A316605 (sigma5), A316606 (sigma6), A316607 (sigma7), A316608 (sigma8), A316609 (sigma9).

%K nonn,cons

%O 1,2

%A _Jean-François Alcover_, Jul 08 2018