A317202 - OEIS

A317202

Decimal expansion of 3 + (t^2+t^4)/2, where t = 0.543689... (A192918) is the real root of x^3 + x^2 + x = 1.

%I #14 May 30 2023 02:23:08

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

%T 2,9,3,4,7,4,6,9,1,0,2,1,8,7,4,2,8,8,0,9,1,0,0,9,7,8,1,3,3,8,6,1,7,6,

%U 8,5,9,4,8,0,0,4,9,7,0,1,4,6,1,1,1

%N Decimal expansion of 3 + (t^2+t^4)/2, where t = 0.543689... (A192918) is the real root of x^3 + x^2 + x = 1.

%C The minimal polynomial of this constant is 2*x^3 - 12*x^2 + 22*x - 13, and it is its unique real root. - _Amiram Eldar_, May 30 2023

%H Bo Tan and Zhi-Ying Wen, <a href="http://dx.doi.org/10.1016/j.ejc.2006.07.007">Some properties of the Tribonacci sequence</a>, European Journal of Combinatorics, 28 (2007) 1703-1719. See Theorem 4.5.

%e 3.191487883953118747061354268227517293474691...

%t RealDigits[x /. FindRoot[2*x^3 - 12*x^2 + 22*x - 13, {x, 3}, WorkingPrecision -> 120]][[1]] (* _Amiram Eldar_, May 30 2023 *)

%Y Cf. A316711, A192918.

%K nonn,cons

%O 1,1

%A _N. J. A. Sloane_, Aug 05 2018