A322159 Decimal expansion of 1 - 1/sqrt(5).

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

Offset: 0

Author

Tristan Cam, Nov 29 2018

Keywords

• cons
• easy
• nonn

Comments

Continued fraction: [0;1,1,4,4,4...].

Least root of the polynomial: 5x^2 - 10x + 4.

Examples

			0.552786404500042060718165266253744752911876328077...
		

Crossrefs

Cf. A001622, A002163, A020762, A081010, A244847, A296182.

Programs

Maple

evalf[110](1-1/sqrt(5)); # Muniru A Asiru, Dec 01 2018

Mathematica

RealDigits[1-1/Sqrt[5], 10, 100][[1]] (* Amiram Eldar, Nov 29 2018 *)

Formula

Equals 1 - 1/A002163.

Equals 1/(1 - cos(4*Pi/5)) = (1/2)*csc(2*Pi/5)^2.

Also equal to 2/(phi*sqrt(5)) = 2/(A001622*A002163).

Equals 1 - A020762. - Andrew Howroyd, Nov 30 2018

From Amiram Eldar, Nov 28 2024: (Start)

Equals 2*A244847 = 1/A296182.

Equals Product_{k>=0} (1 - 1/A081010(k)). (End)