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A318522 Decimal expansion of sqrt(28^(1/3)-27^(1/3)). 1
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 (list; constant; graph; refs; listen; history; text; internal format)
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).

S. Ramanujan, Coll. 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

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 A154490

Adjacent sequences:  A318519 A318520 A318521 * A318523 A318524 A318525

KEYWORD

nonn,cons

AUTHOR

Hugo Pfoertner, Aug 28 2018

STATUS

approved

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Last modified July 15 22:48 EDT 2019. Contains 325061 sequences. (Running on oeis4.)