A318709 - OEIS

%I #16 Aug 06 2024 06:10:45

%S 2,6,2,1,4,0,8,3,8,3,0,7,5,8,6,1,5,0,5,6,9,8,4,9,5,2,8,0,6,1,2,2,4,3,

%T 1,2,7,7,9,7,9,7,0,6,1,4,7,2,1,1,6,7,6,7,9,6,6,4,1,6,7,8,2,5,3,9,3,9,

%U 6,3,1,3,6,7,6,5,7,9

%N Decimal expansion of the solution to x = sqrt(5 + sqrt(5 - sqrt(5 - sqrt(5 + x)))).

%C 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))))".

%H B. C. Berndt, Y. S. Choi, S. Y. Kang, <a href="https://faculty.math.illinois.edu/~berndt/jims.ps">The problems submitted by Ramanujan to the Journal of Indian Math. Soc.</a>, in: Continued fractions, Contemporary Math., 236 (1999), 15-56 (see Q722, JIMS VII).

%H B. C. Berndt, Y. S. Choi, S. Y. Kang, <a href="https://citeseerx.ist.psu.edu/pdf/ae75da0be9fb455e2c55daa5fca46ae63e6a60bd">The problems submitted by Ramanujan to the Journal of Indian Math. Soc.</a>, in: Continued fractions, Contemporary Math., 236 (1999), 15-56 (see Q722, JIMS VII).

%e 2.6214083830758615056984952806122431277979706147211676796641678...

%o (PARI) solve(x=2,3,x-sqrt(5+sqrt(5-sqrt(5-sqrt(5+x)))))

%o (PARI) (1/4)*(sqrt(5)-2+sqrt(13-4*sqrt(5))+sqrt(50+12*sqrt(5)-2*sqrt(65-20*sqrt(5))))

%Y Cf. A286984.

%K nonn,cons

%O 1,1

%A _Hugo Pfoertner_, Sep 01 2018