OFFSET
1,1
COMMENTS
The last part of Ramanujan's question 722 in the Journal of the Indian Mathematical Society (VII, 240) asked "... deduce that, if x = sqrt(5 + sqrt(5 - sqrt(5 - sqrt(5 + x)))), then x = (1/4) * (sqrt(5) - 2 + sqrt(13 - 4 * sqrt(5)) + sqrt(50 + 12 * sqrt(5) - 2 * sqrt(65 - 20 * sqrt(5))))".
LINKS
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).
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
2.6214083830758615056984952806122431277979706147211676796641678...
PROG
(PARI) solve(x=2, 3, x-sqrt(5+sqrt(5-sqrt(5-sqrt(5+x)))))
(PARI) (1/4)*(sqrt(5)-2+sqrt(13-4*sqrt(5))+sqrt(50+12*sqrt(5)-2*sqrt(65-20*sqrt(5))))
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Hugo Pfoertner, Sep 01 2018
STATUS
approved