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%I #10 Nov 17 2020 21:22:59
%S 1,7,5,2,5,1,7,8,2,1,9,2,9,8,1,6,8,1,8,4,8,9,8,3,9,2,1,2,4,3,7,3,1,0,
%T 0,2,7,9,5,2,5,9,0,9,8,8,6,0,6,0,3,1,1,3,3,7,8,5,1,4,2,7,6,0,4,8,4,9,
%U 9,7,7,8,1,3,9,9,0,6,2,2,5,9,7,2,9,5,7,4,9,0,8,4,6,2,5,3,4,4,8
%N Decimal expansion of the negative of the zero x2 of the cubic polynomial x^3 - 2*x^2 - 10*x - 6.
%C For details and links see A335862.
%H Wolfdieter Lang, <a href="https://www.itp.kit.edu/~wl/EISpub/A333852.pdf">A list of representative simple difference sets of the Singer type for small orders m</a>, Karlsruher Institut für Technologie (Karlsruhe, Germany 2020).
%F -x2 = (1/3)*(2 - (1/2)*(1 - sqrt(3)*i)*(179 + 3*sqrt(3)*sqrt(269)*i)^(1/3) - (1/2)*(1 + sqrt(3)*i)*(179 - 3*sqrt(3)*sqrt(269)*i)^(1/3)), where i is the imaginary unit.
%e -x2 = 1.7525178219298168184898392124373100279...
%t With[{j = Sqrt[3] I, k = 3 Sqrt[3] Sqrt[269] I}, First@ RealDigits[Re[(1/3) (2 - (1/2) (1 - j) (179 + k)^(1/3) - (1/2) (1 + j) (179 - k)^(1/3))], 10, 99]] (* _Michael De Vlieger_, Nov 17 2020 *)
%Y Cf. A335862 (x1), A335864 (-x3).
%K nonn,cons,easy
%O 1,2
%A _Wolfdieter Lang_, Jun 29 2020