OFFSET
1,1
COMMENTS
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))), ....".
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
B. C. Berndt, Y. S. Choi, and 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...
MATHEMATICA
RealDigits[(2 + Sqrt[5] + Sqrt[15-6*Sqrt[5]])/2, 10, 120][[1]] (* Amiram Eldar, Jun 27 2023 *)
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
KEYWORD
nonn,cons
AUTHOR
Felix Fröhlich, May 17 2017
STATUS
approved