A318526 - OEIS

A318526

Decimal expansion of (7*20^(1/3)-19)^(1/6).

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

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OFFSET

0,1

COMMENTS

Ramanujan's question 1076 (i), see Berndt and Rankin in References: Show that (7*20^(1/3)-19)^(1/6) = (5/3)^(1/3)-(2/3)^(1/3).

REFERENCES

B. C. Berndt and R. A. Rankin, Ramanujan: Essays and Surveys, American Mathematical Society, 2001, ISBN 0-8218-2624-7, page 222 (JIMS 11, page 199).

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 334, Question 1076

LINKS

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

EXAMPLE

0.31205063676038873295483111393230510491288642292526830038794456442743462...

MAPLE

evalf((7*20^(1/3)-19)^(1/6)); # Muniru A Asiru, Aug 28 2018

MATHEMATICA

RealDigits[Surd[7 Surd[20, 3]-19, 6], 10, 120][[1]] (* Harvey P. Dale, Dec 07 2021 *)

PROG

(PARI) (7*20^(1/3)-19)^(1/6)

CROSSREFS