A316605 Decimal expansion of the fifth smallest known Salem number.

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

Index entries for algebraic numbers, degree 10.

Formula

Minimal polynomial 1 - x^4 - x^5 - x^6 + x^10.

Example

1.21639166113826509162680631119946332772225360657057075756042706583831...

Mathematica

c1 = {1, 0, 0, 0, -1, -1};
c2 = Join[c1, Reverse[Most[c1]]];
p = (x^Range[0, Length[c2] - 1]).c2;
sigma5 = Root[p, x, 2];
RealDigits[sigma5, 10, 102][[1]]

Prog

(PARI) polrootsreal(1 - x^4 - x^5 - x^6 + x^10)[2] \\ Charles R Greathouse IV, Feb 11 2025

Crossrefs

Cf. A073011 (sigma1), A219300 (sigma2), A306078 (sigma3), A306079 (sigma4), A316606 (sigma6), A316607 (sigma7), A316608 (sigma8), A316609 (sigma9), A316610 (sigma10). Cf. A316605 (other root)

Sequence in context: A284475 A353660 A285355 * A307178 A343611 A026191

Adjacent sequences: A316602 A316603 A316604 * A316606 A316607 A316608

Keyword

nonn,cons

Author

Jean-François Alcover, Jul 08 2018

Status

approved