

A239797


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


2



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, 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, 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
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OFFSET

1,3


COMMENTS

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.)
An algebraic number of degree 6.  Charles R Greathouse IV, Apr 14 2014


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000
William Stein, Algebraic Number Theory, a Computational Approach, p. 69 (in the PDF), Example 6.1.1, or Discriminants and Norms chapter (HTML).


FORMULA

2^(1/3)/2 = 1/2^(2/3) = 1/4^(1/3).
(2^(1/3)/2 + sqrt(3)/4^(1/3))^3 = 2.
Equals Product_{n >= 1} 1/(1  1/(6*n  2)^2 ).  Fred Daniel Kline, Dec 19 2015


EXAMPLE

1.0911236359717214...


MATHEMATICA

RealDigits[Sqrt[3]/4^(1/3), 10, 100][[1]]


PROG

(PARI) polrootsreal(16*x^627)[2] \\ Charles R Greathouse IV, Apr 14 2014


CROSSREFS

Cf. A235362.
Sequence in context: A322029 A322107 A180839 * A010163 A200128 A225537
Adjacent sequences: A239794 A239795 A239796 * A239798 A239799 A239800


KEYWORD

cons,nonn


AUTHOR

Alonso del Arte, Mar 27 2014


STATUS

approved



