A316606 Decimal expansion of the sixth smallest known Salem number.

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

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

Equals root of p = 1 - x - x^8 + x^9 - x^10 - x^17 + x^18 with largest absolute value.

Example

1.219720859040311844169606760414677944390415505541569678287974417873...

Mathematica

c1 = {1, -1, 0, 0, 0, 0, 0, 0, -1, 1};
c2 = Join[c1, Reverse[Most[c1]]];
p = (x^Range[0, Length[c2] - 1]).c2;
sigma6 = Root[p, x, 2];
RealDigits[sigma6, 10, 102][[1]]

Crossrefs

Cf. A073011 (sigma1), A219300 (sigma2), A306078 (sigma3 ), A306079 (sigma4), A316605 (sigma5), A316607 (sigma7), A316608 (sigma8), A316609 (sigma9), A316610 (sigma10).

Sequence in context: A245461 A086572 A349035 * A016632 A176400 A021459

Adjacent sequences: A316603 A316604 A316605 * A316607 A316608 A316609

Keyword

nonn,cons

Author

Jean-François Alcover, Jul 08 2018

Status

approved