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%I #29 May 01 2023 09:44:32
%S 1,6,9,5,6,2,0,7,6,9,5,5,9,8,6,2,0,5,7,4,1,6,3,6,7,1,0,0,1,1,7,5,3,5,
%T 3,4,2,6,1,8,1,7,9,3,8,8,2,0,8,5,0,7,7,3,0,2,2,1,8,7,0,7,2,8,4,4,5,2,
%U 4,4,5,3,4,5,4,0,8,0,0,7,2,2,1,3,9,9
%N Decimal expansion of the real root of x^3 - x^2 - 2 = 0.
%D D. E. Daykin and S. J. Tucker, Introduction to Dragon Curves, unpublished, 1976, end of section 2. See links in A003229.
%H Angel Chang and Tianrong Zhang, <a href="http://www.coiraweb.com/poignance/math/Fractals/Dragon/Bound.html">The Fractal Geometry of the Boundary of Dragon Curves</a>, Journal of Recreational Mathematics, volume 30, number 1, 1999-2000, pages 9-22.
%F r = D^(1/3) + (1/9)*D^(-1/3) + 1/3 where D = 28/27 + (1/9)*sqrt(29*3) [Chang and Zhang] from the usual cubic solution formula. Or similarly r = (1/3)*(1 + C + 1/C) where C = (28 + sqrt(29*27))^(1/3). - _Kevin Ryde_, Oct 25 2019
%e 1.6956207695598620574163671001175353426181793882085077...
%t z = 2000; r = 8/5;
%t u = CoefficientList[Series[1/Sum[Floor[(k + 1)*r] (-x)^k, {k, 0, z}], {x, 0, z}], x]; (* A289260 *)
%t v = N[u[[z]]/u[[z - 1]], 200]
%t RealDigits[v, 10][[1]] (* A289265 *)
%o (PARI) solve(x=1, 2, x^3 - x^2 - 2) \\ _Michel Marcus_, Oct 26 2019
%Y Sequences growing as this power: A003229, A003476, A003479, A052537, A077949, A144181, A164395, A164399, A164410, A164414, A164471, A203175, A227036, A289260, A292764.
%Y Cf. A078140 (includes guide to constants similar to A289260).
%K nonn,cons,easy
%O 1,2
%A _Clark Kimberling_, Jul 14 2017
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