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%I #20 Jun 26 2023 02:22:12
%S 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,
%T 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,
%U 2,5,5,8,0,8,3,1,6,9,3,3,8,7,1,6,9
%N Decimal expansion of sqrt(5^(1/3)-4^(1/3)).
%C 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.
%D 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).
%D Srinivasa Ramanujan, Collected Papers, Chelsea, 1962, page 327, Question 525.
%H Susan Landau, <a href="https://doi.org/10.1137/0221009">Simplification of nested radicals</a>, 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.]
%e 0.35010697609230455692617090560659825894828686636319163198125568162868255...
%p evalf(sqrt(5^(1/3)-4^(1/3))); # _Muniru A Asiru_, Aug 28 2018
%t RealDigits[Sqrt[Surd[5, 3] - Surd[4, 3]], 10, 120][[1]] (* _Amiram Eldar_, Jun 26 2023 *)
%o (PARI) sqrt(5^(1/3)-4^(1/3))
%Y Cf. A318522.
%K nonn,cons
%O 0,1
%A _Hugo Pfoertner_, Aug 28 2018
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