A020832 Decimal expansion of 1/sqrt(75).

1, 1, 5, 4, 7, 0, 0, 5, 3, 8, 3, 7, 9, 2, 5, 1, 5, 2, 9, 0, 1, 8, 2, 9, 7, 5, 6, 1, 0, 0, 3, 9, 1, 4, 9, 1, 1, 2, 9, 5, 2, 0, 3, 5, 0, 2, 5, 4, 0, 2, 5, 3, 7, 5, 2, 0, 3, 7, 2, 0, 4, 6, 5, 2, 9, 6, 7, 9, 5, 5, 3, 4, 4, 6, 0, 5, 8, 6, 6, 6, 9, 1, 3, 8, 7, 4, 3, 0, 7, 9, 1, 1, 7, 1, 4, 9, 9, 0, 5

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cons
• easy

Comments

Multiplied by 10 this is 2/sqrt(3). - Alonso del Arte, Apr 30 2012

2/sqrt(3) is Hermite's constant gamma_2. - Jean-François Alcover, Sep 02 2014, after Steven Finch.

2/sqrt(3) is the Lorentz factor for an object traveling at half the speed of light. - Sean Stroud, May 05 2019

Examples

			0.1154700538379251529...
		

Links

• Ivan Panchenko, Table of n, a(n) for n = 0..1000
• Steven R. Finch, Errata and Addenda to Mathematical Constants, arXiv:2001.00578 [math.HO], 2020, p. 62.
• Yining Hu, Patterns in numbers and infinite sums and products, arXiv:1506.00151 [math.NT], 2015.
• Samuel G. Moreno and Esther M. García, New Infinite Products of Cosines and Viète-Like Formulae, Mathematics Magazine, vol. 86, no. 1, 2013, pp. 15-25. See formula for 2/sqrt(3) page 15.
• Index entries for algebraic numbers, degree 2

Crossrefs

Cf. A010153 (continued fraction, but missing the initial 0), A047235.

Programs

Mathematica

RealDigits[1/Sqrt[75], 10, 100][[1]] (* Alonso del Arte, Apr 30 2012 *)

PARI

75^-.5 \\ Charles R Greathouse IV, Mar 31 2016

Formula

(csc(Pi/3))/10, where csc is the cosecant function. - Alonso del Arte, Apr 30 2012

Product_{n>=1} ((3*n+1)/(3*n+2))^((-1)^n), with offset 1. (see Hu link). - Michel Marcus, Jun 02 2015

From Amiram Eldar, Aug 02 2020: (Start)

2/sqrt(3) = Sum_{k>=0} binomial(2*k,k)/16^k.

2/sqrt(3) = 1 + Sum_{k>=1} (2*k-1)!!/((2*k)!! * 2^(2*k)). (End)

2/sqrt(3) = Product_{k>=1} (1 - (-1)^k/A047235(k)). - Amiram Eldar, Nov 22 2024