A152422 Decimal expansion of (sqrt(3)-1)/2.

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

Offset: 0

Author

Geoffrey Caveney, Dec 03 2008

Keywords

• nonn
• cons
• easy

Comments

The number has continued fraction [0, 2, 1, 2, 1, 2, 1, ...].

The iterated function z^2 - 1/2 gives a good rational approximation of this number times -1 after sixty steps. - Alonso del Arte, Apr 10 2016

Examples

			0.36602540378443864676372317...
		

Crossrefs

A variant of A010527, which is the main entry. - N. J. A. Sloane, Dec 04 2008

Programs

Maple

Digits:=100; evalf((sqrt(3)-1)/2); # Wesley Ivan Hurt, Apr 18 2014

Mathematica

RealDigits[(Sqrt[3] - 1)/2, 10, 100] [[1]] (* Wesley Ivan Hurt, Apr 18 2014 *)

PARI

(sqrt(3)-1)/2 \\ Altug Alkan, Apr 11 2016

Formula

Equals Product_{k>=1} (1 + (-1)^k * 2/(6*k-3)). - Amiram Eldar, Aug 10 2020

Extensions

a(98) corrected by Georg Fischer, Apr 03 2020