A316608 Decimal expansion of the eighth smallest known Salem number.

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, 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, 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

Offset

1,2

Links

Table of n, a(n) for n=1..102.

M. J. Mossinghoff, Small Salem Numbers

Eric Weisstein's MathWorld, Salem Constants.

Wikipedia, Salem number

Formula

p = 1 - x - x^5 + x^6 - x^9 + x^10 - x^11 + x^14 - x^15 - x^19 + x^20.

Example

1.2326135485931210039627316948079097914115773712098310467299165820538...

Mathematica

c1 = {1, -1, 0, 0, 0, -1, 1, 0, 0, -1, 1};
c2 = Join[c1, Reverse[Most[c1]]];
p = (x^Range[0, Length[c2] - 1]).c2;
sigma8 = Root[p, x, 2];
RealDigits[sigma8, 10, 102][[1]]

Crossrefs

Cf. A073011 (sigma1), A219300 (sigma2), A306078 (sigma3 ), A306079 (sigma4), A316605 (sigma5), A316606 (sigma6), A316607 (sigma7), A316609 (sigma9), A316610 (sigma10).

Sequence in context: A078599 A183103 A183105 * A033031 A134060 A329282

Adjacent sequences: A316605 A316606 A316607 * A316609 A316610 A316611

Keyword

nonn,cons

Author

Jean-François Alcover, Jul 08 2018

Status

approved