A296182 Decimal expansion of (2 + phi)/2, with the golden section phi from A001622.

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

Offset: 1

Author

Wolfdieter Lang, Jan 08 2018

Keywords

• nonn
• cons
• easy

Comments

In a regular pentagon this is the distance between a vertex and the midpoint of the opposite side in units of the radius of the circumscribing circle.

Examples

			1.809016994374947424102293417182819058860154589902881431067724311352630231409451...
		

Links

• Index entries for algebraic numbers, degree 2.

Crossrefs

Cf. A001622, A019863, A081003, A322159.

Programs

Mathematica

RealDigits[(5 + Sqrt[5])/4, 10, 111][[1]] (* Robert G. Wilson v, Jan 14 2018 *)
RealDigits[(2+GoldenRatio)/2,10,120][[1]] (* Harvey P. Dale, Aug 10 2025 *)

PARI

(5 + sqrt(5))/4 \\ Michel Marcus, Jan 08 2018

Formula

Equals (2 + phi)/2 = (5 + sqrt(5))/4 = (2*phi - 1)*phi/2 = with phi from A001622.

Equals 1 + A019863.

From Amiram Eldar, Nov 28 2024: (Start)

Equals 1/A322159.

Equals Product_{k>=0} (1 + 1/A081003(k)). (End)