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A239797 Decimal expansion of square root of 3 divided by cube root of 4.

%I A239797 #30 Aug 21 2023 11:39:53
%S A239797 1,0,9,1,1,2,3,6,3,5,9,7,1,7,2,1,4,0,3,5,6,0,0,7,2,6,1,4,1,8,9,8,0,8,
%T A239797 8,8,1,3,2,5,8,7,3,3,3,8,7,4,0,3,0,0,9,4,0,7,0,3,6,4,1,0,7,3,2,3,6,7,
%U A239797 8,0,1,1,0,0,5,7,2,2,3,7,4,2,0,3,3,3,3,0,0,8,3,8,2,1,7,7
%N A239797 Decimal expansion of square root of 3 divided by cube root of 4.
%C A239797 This is the principal square root of 3 divided by the principal cube root of 4. This number is the imaginary part of a complex cubic root of 2, namely -2^(1/3)/2 + sqrt(-3)/4^(1/3). (The other complex cubic root of 2 is the same except for the sign of the imaginary part.)
%C A239797 An algebraic number of degree 6. - _Charles R Greathouse IV_, Apr 14 2014
%H A239797 G. C. Greubel, <a href="/A239797/b239797.txt">Table of n, a(n) for n = 1..10000</a>
%H A239797 William Stein, <a href="http://sage.math.washington.edu/home/wstein/www/books/ant/">Algebraic Number Theory, a Computational Approach</a>, p. 69 (in the PDF), Example 6.1.1, or <a href="http://sage.math.washington.edu/home/wstein/www/books/ant/ant/node40.html">Discriminants and Norms chapter</a> (HTML).
%H A239797 <a href="/index/Al#algebraic_06">Index entries for algebraic numbers, degree 6</a>
%F A239797 2^(1/3)/2 = 1/2^(2/3) = 1/4^(1/3).
%F A239797 (-2^(1/3)/2 + sqrt(-3)/4^(1/3))^3 = 2.
%F A239797 Equals Product_{n >= 1} 1/(1 - 1/(6*n - 2)^2 ). - _Fred Daniel Kline_, Dec 19 2015
%e A239797 1.0911236359717214...
%t A239797 RealDigits[Sqrt[3]/4^(1/3), 10, 100][[1]]
%o A239797 (PARI) polrootsreal(16*x^6-27)[2] \\ _Charles R Greathouse IV_, Apr 14 2014
%Y A239797 Cf. A235362.
%K A239797 cons,nonn
%O A239797 1,3
%A A239797 _Alonso del Arte_, Mar 27 2014