A318522 Decimal expansion of sqrt(28^(1/3)-27^(1/3)).

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

Offset

0,2

Comments

Ramanujan's question 525 (ii), see Berndt and Rankin in References: Show how to find the square roots of surds of the form A^(1/3) + B^(1/3), and hence prove that sqrt(28^(1/3)-27^(1/3)) = (98^(1/3)-28^(1/3)-1)/3.

Real root of x^3 + x^2 + 5*x - 1 = 0. - Hugo Pfoertner, Sep 12 2018

References

B. C. Berndt and R. A. Rankin, Ramanujan: Essays and Surveys, American Mathematical Society, 2001, ISBN 0-8218-2624-7, page 221 (JIMS 6, page 39 and pages 191-192).

Srinivasa Ramanujan, Collected Papers, Chelsea, 1962, page 327, Question 525.

Links

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

Example

0.191282440060928016751295506478335098972307207254571910553771150812505...

Maple

evalf(sqrt(28^(1/3)-27^(1/3))); # Muniru A Asiru, Aug 28 2018

Mathematica

RealDigits[Sqrt[28^(1/3) - 27^(1/3)], 10, 120][[1]] (* Amiram Eldar, Jun 27 2023 *)

Prog

(PARI) sqrt(28^(1/3)-27^(1/3))
(PARI) p(x)=x^3+x^2+5*x-1;
solve(x=0.18, 0.20, p(x)) \\ Hugo Pfoertner, Sep 12 2018

Crossrefs

Cf. A318521.

Sequence in context: A197830 A068151 A199378 * A005482 A080504 A327958

Adjacent sequences: A318519 A318520 A318521 * A318523 A318524 A318525

Keyword

nonn,cons

Author

Hugo Pfoertner, Aug 28 2018

Status

approved