A318523 - OEIS

%I #9 Dec 14 2021 15:00:52

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

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

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

%N Decimal expansion of sqrt((1/5)^(1/5)+(4/5)^(1/5)).

%C Ramanujan's question 1070 (i) asks for a proof of the identities

%C sqrt((1/5)^(1/5)+(4/5)^(1/5)) = (1+2^(1/5)+8^(1/5))^(1/5) = (16/125)^(1/5)+(8/125)^(1/5)+(2/125)^(1/5)-(1/125)^(1/5).

%D S. Ramanujan, Coll. Papers, Chelsea, 1962, page 334, Question 1070.

%e 1.296584807665018307492401645829135777485135213485302261427431418...

%t RealDigits[Sqrt[Surd[1/5,5]+Surd[4/5,5]],10,120][[1]] (* _Harvey P. Dale_, Dec 14 2021 *)

%o (PARI) sqrt((1/5)^(1/5)+(4/5)^(1/5))

%Y Cf. A318524, A318525.

%K nonn,cons

%O 1,2

%A _Hugo Pfoertner_, Aug 28 2018