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A286984 Decimal expansion of (2 + sqrt(5) + sqrt(15 - 6*sqrt(5)))/2. 1
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See Question 722 on page 219 of Berndt, 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))), ....".

A quartic integer with minimal polynomial x^4 - 4x^3 - 4x^2 + 31x - 29. - Charles R Greathouse IV, May 17 2017

REFERENCES

B. C. Berndt and R. A. Rankin, Ramanujan: Essays and Surveys, American Mathematical Society, 2001, ISBN 0-8218-2624-7.

LINKS

Table of n, a(n) for n=1..87.

B. C. Berndt, Y. S. Choi, S. Y. Kang, The problems submitted by Ramanujan to the Journal of Indian Math. Soc., in: Continued fractions, Contemporary Math., 236 (1999), 15-56 (see Q722, JIMS VII).

EXAMPLE

2.74723827493230433305746518613420282675...

PROG

(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

CROSSREFS

Cf. A239349, A318709.

Sequence in context: A197143 A132724 A175641 * A021368 A019968 A257434

Adjacent sequences:  A286981 A286982 A286983 * A286985 A286986 A286987

KEYWORD

nonn,cons

AUTHOR

Felix Fröhlich, May 17 2017

STATUS

approved

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Last modified October 19 13:38 EDT 2018. Contains 316361 sequences. (Running on oeis4.)