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A289265 Decimal expansion of the real root of x^3 - x^2 - 2 = 0. 3
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 (list; constant; graph; refs; listen; history; text; internal format)
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D. E. Daykin and S. J. Tucker, Introduction to Dragon Curves, unpublished, 1976, end of section 2.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

Table of n, a(n) for n=1..86.

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.

Index entries for linear recurrences with constant coefficients, signature (1,0,2).

Index entries for linear recurrences with constant coefficients, signature (2,-1,2,-2)

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]](* A289065 *)

PROG

(PARI) solve(x=1, 2, x^3 - x^2 - 2) \\ Michel Marcus, Oct 26 2019

CROSSREFS

Sequences growing as this power: A003229, A003476, A003479, A052537, A077949, A144181, A164395, A164399, A164410, A164414, A164471, A203175, A227036, A289260

Cf. A078140 (includes guide to constants similar to A289260).

Sequence in context: A199445 A201297 A259928 * A301869 A198818 A335204

Adjacent sequences:  A289262 A289263 A289264 * A289266 A289267 A289268

KEYWORD

nonn,cons,easy

AUTHOR

Clark Kimberling, Jul 14 2017

STATUS

approved

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Last modified September 21 09:44 EDT 2020. Contains 337268 sequences. (Running on oeis4.)