A318709 Decimal expansion of the solution to x = sqrt(5 + sqrt(5 - sqrt(5 - sqrt(5 + x)))).

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, 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, 6, 3, 1, 3, 6, 7, 6, 5, 7, 9

Offset: 1

Author

Hugo Pfoertner, Sep 01 2018

Keywords

• nonn
• cons

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))))".

Examples

			2.6214083830758615056984952806122431277979706147211676796641678...
		

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).

Crossrefs

Cf. A286984.

Programs

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))))