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

Author

Jean-François Alcover, Jul 08 2018

Keywords

• nonn
• cons

Examples

			1.21639166113826509162680631119946332772225360657057075756042706583831...
		

Links

• M. J. Mossinghoff, Small Salem Numbers
• Eric Weisstein's MathWorld, Salem Constants.
• Wikipedia, Salem number
• Index entries for algebraic numbers, degree 10.

Crossrefs

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

Programs

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]]

PARI

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

Formula

p = 1 - x^4 - x^5 - x^6 + x^10.