A318524 Decimal expansion of ((32/5)^(1/5)-(27/5)^(1/5))^(1/3).

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

Offset

0,1

Comments

Ramanujan's question 1070 (ii) asks for a proof of the identity

((32/5)^(1/5)-(27/5)^(1/5))^(1/3) = (1/25)^(1/5)+(3/25)^(1/5)-(9/25)^(1/5).

References

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

Links

Table of n, a(n) for n=0..84.

Index entries for algebraic numbers, degree 25.

Formula

Minimal polynomial: x^25 - 5*x^20 - 5*x^15 + 65*x^10 + 155*x^5 - 1. - Amiram Eldar, Jun 12 2026

Example

0.36450184121606803517626067446520737637319536517131414493623272802...

Mathematica

RealDigits[Surd[Surd[32/5, 5]-Surd[27/5, 5], 3], 10, 120][[1]] (* Harvey P. Dale, Oct 08 2018 *)

Prog

(PARI) ((32/5)^(1/5)-(27/5)^(1/5))^(1/3)

Crossrefs

Cf. A318523, A318525.

Sequence in context: A351124 A159354 A196500 * A155530 A249032 A251534

Adjacent sequences: A318521 A318522 A318523 * A318525 A318526 A318527

Keyword

nonn,cons,changed

Author

Hugo Pfoertner, Aug 28 2018

Status

approved