%I #8 Jan 12 2023 01:50:50

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

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

%U 6,6,0,6,3,9,8,6,8,0

%N Decimal expansion of the real root of 3*x^3 - 2.

%C This number is the reciprocal of A319034.

%C The other (complex) roots are, with the present number r = (2/3)^(1/3), r*w = -0.4367902323... + 0.7565428747...*i, and its conjugate, where w = exp(2*Pi*i/3) = (-1 + sqrt(3)*i)/2 is one of the complex roots of x^3 - 1.

%F r = (2/3)^(1/3) = 1/A319034 = (1/3)*18^(1/3) = (1/3)*A010590.

%e 0.87358046473629886904722042681399875674647588190787724170092460190956...

%t RealDigits[Surd[2/3, 3], 10, 100][[1]] (* _Amiram Eldar_, Jan 05 2023 *)

%o (PARI) (2/3)^(1/3) \\ _Michel Marcus_, Jan 05 2023

%Y Cf. A010590, A319034.

%K nonn,cons,easy

%O 0,1

%A _Wolfdieter Lang_, Jan 02 2023