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).

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.]

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