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

Author

Alonso del Arte, Mar 27 2014

Keywords

• cons
• nonn

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

Examples

			1.0911236359717214...
		

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

Crossrefs

Cf. A235362.

Programs

Mathematica

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

PARI

polrootsreal(16*x^6-27)[2] \\ Charles R Greathouse IV, Apr 14 2014

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