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A318521 Decimal expansion of sqrt(5^(1/3)-4^(1/3)). 1
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 (list; constant; graph; refs; listen; history; text; internal format)
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).

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.]

S. Ramanujan, Coll. Papers, Chelsea, 1962, page 327, Question 525.

LINKS

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

EXAMPLE

0.35010697609230455692617090560659825894828686636319163198125568162868255...

MAPLE

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

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

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Last modified December 13 22:55 EST 2019. Contains 329974 sequences. (Running on oeis4.)