A275933 Decimal expansion of constant related to complexity of the tribonacci word (A080843).

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

Offset: 2

Author

N. J. A. Sloane, Sep 02 2016

Keywords

• nonn
• cons

Comments

The minimal polynomial of this constant is x^3 - 13*x^2 + 27*x - 17, and it is its unique real root. - Amiram Eldar, May 27 2023

Examples

			10.6052382910266361207972696375...
		

Links

• Nataliya Chekhova, Pascal Hubert, and Ali Messaoudi, Propriétés combinatoires, ergodiques et arithmétiques de la substitution de Tribonacci, Journal de théorie des nombres de Bordeaux, 13.2 (2001): 371-394.

Crossrefs

Cf. A080843, A058265.

Programs

Mathematica

RealDigits[x /. FindRoot[x^3 - 13*x^2 + 27*x - 17, {x, 10}, WorkingPrecision -> 120]][[1]] (* Amiram Eldar, May 27 2023 *)

Formula

Equals 9+(6*t-4)/(t^2+1), where t is the tribonacci constant A058265.

Equals (13 + (847 - 33*sqrt(33))^(1/3) + (11 * (77 + 3*sqrt(33)))^(1/3))/3. - Amiram Eldar, May 27 2023

Extensions

More terms from Joerg Arndt, Sep 02 2016