A318521 Decimal expansion of sqrt(5^(1/3)-4^(1/3)).

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

Offset

0,1

Comments

Ramanujan's question 525 (i), 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(5^(1/3)-4^(1/3)) = (2^(1/3)+20^(1/3)-25^(1/3))/3.

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).

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, Section 1.1.2, p. 4.

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

Links

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

Susan Landau, Simplification of nested radicals, SIAM Journal on Computing 21.1 (1992): 85-110. See page 85. [Do not confuse this paper with the short FOCS conference paper with the same title, which is only a few pages long.]

Formula

Minimal polynomial: 1 - 23*x^3 - 7*x^6 - x^9. - Stefano Spezia, Oct 15 2024

Example

0.35010697609230455692617090560659825894828686636319163198125568162868255...

Maple

evalf(sqrt(5^(1/3)-4^(1/3))); # Muniru A Asiru, Aug 28 2018

Mathematica

RealDigits[Sqrt[Surd[5, 3] - Surd[4, 3]], 10, 120][[1]] (* Amiram Eldar, Jun 26 2023 *)

Prog

(PARI) sqrt(5^(1/3)-4^(1/3))

Crossrefs

Cf. A318522.

Sequence in context: A113037 A063866 A059106 * A087676 A291207 A058813

Adjacent sequences: A318518 A318519 A318520 * A318522 A318523 A318524

Keyword

nonn,cons

Author

Hugo Pfoertner, Aug 28 2018

Status

approved