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Decimal expansion of t^3, where t is the tribonacci constant A058265.
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%I #32 Nov 28 2023 11:00:52

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

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

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

%N Decimal expansion of t^3, where t is the tribonacci constant A058265.

%C A cubic integer with minimal polynomial x^3 - 7x^2 + 5x - 1, of which it is the unique real root. - _Charles R Greathouse IV_, Nov 06 2016

%H <a href="/index/Al#algebraic_03">Index entries for algebraic numbers, degree 3</a>

%F 1/t + 1/t^2 + 1/t^3 = 1/A058265 + 1/A276800 + 1/A276801 = 1.

%F From _Dimitri Papadopoulos_, Nov 07 2023: (Start)

%F t^3 = (A276800^2 + 1)/2.

%F t^3 + 1/t^3 = t + 1/t + 4.

%F t^3 = (1/4)*(t + 1)^2*(t - 1)^2*(t^2 + 1). (End)

%e 6.222262523120398626674561101108321187373560789846168428798321316639575...

%t RealDigits[x /. FindRoot[x^3 - 7*x^2 + 5*x - 1, {x, 6}, WorkingPrecision -> 120]][[1]] (* _Amiram Eldar_, May 27 2023 *)

%o (PARI) polrootsreal(x^3-7*x^2+5*x-1)[1] \\ _Charles R Greathouse IV_, Nov 06 2016

%Y Cf. A058265, A276800.

%K nonn,cons

%O 1,1

%A _N. J. A. Sloane_, Oct 28 2016