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

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

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).

Index entries for algebraic numbers, degree 6

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^6-27)[2] \\ Charles R Greathouse IV, Apr 14 2014

Crossrefs

Cf. A235362.

Sequence in context: A322107 A180839 A272232 * A010163 A200128 A225537

Adjacent sequences: A239794 A239795 A239796 * A239798 A239799 A239800

Keyword

cons,nonn

Author

Alonso del Arte, Mar 27 2014

Status

approved