A318523 Decimal expansion of sqrt((1/5)^(1/5)+(4/5)^(1/5)).

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

Offset

1,2

Comments

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

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).

References

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

Links

Table of n, a(n) for n=1..86.

Index entries for algebraic numbers, degree 25.

Formula

Minimal polynomial: x^25 - 5*x^20 + 10*x^15 - 20*x^10 + 5*x^5 - 1. - Amiram Eldar, May 28 2026

Example

1.296584807665018307492401645829135777485135213485302261427431418...

Mathematica

RealDigits[Sqrt[Surd[1/5, 5]+Surd[4/5, 5]], 10, 120][[1]] (* Harvey P. Dale, Dec 14 2021 *)

Prog

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

Crossrefs

Cf. A318524, A318525.

Sequence in context: A011069 A010598 A152564 * A138029 A146481 A233766

Adjacent sequences: A318520 A318521 A318522 * A318524 A318525 A318526

Keyword

nonn,cons

Author

Hugo Pfoertner, Aug 28 2018

Status

approved