A275933 - OEIS

%I #20 May 27 2023 04:15:52

%S 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,

%T 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,

%U 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

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

%C 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

%H Nataliya Chekhova, Pascal Hubert, and Ali Messaoudi, <a href="http://www.numdam.org/item?id=JTNB_2001__13_2_371_0">Propriétés combinatoires, ergodiques et arithmétiques de la substitution de Tribonacci</a>, Journal de théorie des nombres de Bordeaux, 13.2 (2001): 371-394.

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

%F Equals (13 + (847 - 33*sqrt(33))^(1/3) + (11 * (77 + 3*sqrt(33)))^(1/3))/3. - _Amiram Eldar_, May 27 2023

%e 10.6052382910266361207972696375...

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

%Y Cf. A080843, A058265.

%K nonn,cons

%O 2,3

%A _N. J. A. Sloane_, Sep 02 2016

%E More terms from _Joerg Arndt_, Sep 02 2016