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A286984
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Decimal expansion of (2 + sqrt(5) + sqrt(15 - 6*sqrt(5)))/2.
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1
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2, 7, 4, 7, 2, 3, 8, 2, 7, 4, 9, 3, 2, 3, 0, 4, 3, 3, 3, 0, 5, 7, 4, 6, 5, 1, 8, 6, 1, 3, 4, 2, 0, 2, 8, 2, 6, 7, 5, 8, 1, 6, 3, 8, 7, 8, 7, 7, 6, 1, 6, 7, 9, 8, 7, 7, 8, 3, 8, 0, 4, 3, 7, 3, 8, 5, 6, 2, 2, 4, 3, 6, 4, 8, 5, 3, 8, 3, 0, 1, 5, 0, 3, 4, 3, 1, 5
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OFFSET
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1,1
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COMMENTS
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See Question 722 on page 219 of Berndt and Rankin, 2001. This says, in part: "Solve completely x^2 = a + y, y^2 = a + z, z^2 = a + u, u^2 = a + x and deduce that, if x = sqrt(5 + sqrt(5 + sqrt(5 - sqrt(5 + x)))), then x = 1/2(2 + sqrt(5) + sqrt(15 - 6*sqrt(5))), ....".
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REFERENCES
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B. C. Berndt and R. A. Rankin, Ramanujan: Essays and Surveys, American Mathematical Society, 2001, ISBN 0-8218-2624-7.
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LINKS
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EXAMPLE
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2.74723827493230433305746518613420282675...
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MATHEMATICA
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RealDigits[(2 + Sqrt[5] + Sqrt[15-6*Sqrt[5]])/2, 10, 120][[1]] (* Amiram Eldar, Jun 27 2023 *)
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PROG
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(PARI) default(realprecision, 90); (2+sqrt(5)+sqrt(15-6*sqrt(5)))/2
(PARI) solve(x=2, 3, x-sqrt(5+sqrt(5+sqrt(5-sqrt(5 + x))))) // Hugo Pfoertner, Sep 02 2018
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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