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A289265
Decimal expansion of the real root of x^3 - x^2 - 2 = 0.
6
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, 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, 4, 4, 5, 3, 4, 5, 4, 0, 8, 0, 0, 7, 2, 2, 1, 3, 9, 9
OFFSET
1,2
REFERENCES
D. E. Daykin and S. J. Tucker, Introduction to Dragon Curves, unpublished, 1976, end of section 2. See links in A003229.
LINKS
Angel Chang and Tianrong Zhang, The Fractal Geometry of the Boundary of Dragon Curves, Journal of Recreational Mathematics, volume 30, number 1, 1999-2000, pages 9-22.
FORMULA
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
EXAMPLE
1.6956207695598620574163671001175353426181793882085077...
MATHEMATICA
z = 2000; r = 8/5;
u = CoefficientList[Series[1/Sum[Floor[(k + 1)*r] (-x)^k, {k, 0, z}], {x, 0, z}], x]; (* A289260 *)
v = N[u[[z]]/u[[z - 1]], 200]
RealDigits[v, 10][[1]] (* A289265 *)
PROG
(PARI) solve(x=1, 2, x^3 - x^2 - 2) \\ Michel Marcus, Oct 26 2019
CROSSREFS
Cf. A078140 (includes guide to constants similar to A289260).
Sequence in context: A346367 A201297 A259928 * A301869 A198818 A335204
KEYWORD
nonn,cons,easy
AUTHOR
Clark Kimberling, Jul 14 2017
STATUS
approved