A306078 Decimal expansion of the third smallest known Salem number.

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

Offset

1,2

Links

Table of n, a(n) for n=1..100.

M. J. Mossinghoff, Small Salem Numbers

Eric Weisstein's MathWorld, Salem Constants.

Wikipedia, Salem number

Index entries for algebraic numbers, degree 14.

Example

1.200026523987391518902962100414601567240618151999851067924399839886...

Mathematica

c1 = {1, 0, 0, -1, -1, 0, 0, 1};
c2 = Join[c1, Reverse[Most[c1]]];
p = (x^Range[0, Length[c2]-1]). c2;
sigma3 = Root[p, x, 2];
RealDigits[sigma3, 10, 100][[1]]

Prog

(PARI) polrootsreal(x^14 - x^11 - x^10 + x^7 - x^4 - x^3 + 1)[2] \\ Charles R Greathouse IV, Feb 11 2025

Crossrefs

Cf. A073011 (sigma1), A219300 (sigma2), A306079 (sigma4).

Sequence in context: A345940 A076998 A173956 * A284273 A083927 A154724

Adjacent sequences: A306075 A306076 A306077 * A306079 A306080 A306081

Keyword

nonn,cons

Author

Jean-François Alcover, Jun 19 2018

Status

approved