A187798 Decimal expansion of (3-phi)/2, where phi is the golden ratio.

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

Offset

0,1

Comments

This is the height h of the isosceles triangle in a regular pentagon inscribed in the unit circle formed from a diagonal as base and two adjacent pentagon sides. h = sqrt(sqrt(3-phi)^2 - (sqrt(2 + phi)/2)^2) = sqrt(10 - 5*phi)/2 = (3 - phi)/2. - Wolfdieter Lang, Jan 07 2018

Links

Ivan Panchenko, Table of n, a(n) for n = 0..1000

Index entries for algebraic numbers, degree 2.

Formula

Equals (3-phi)/2 = A094874/2 with phi from A001622.

From Amiram Eldar, Nov 28 2024: (Start)

Equals 1/A344212.

Equals Product_{k>=0} (1 - 1/A081011(k)). (End)

Example

0.6909830056250525758977065828171809411398454100971185689322756886473697685905...

Mathematica

RealDigits[(3 - GoldenRatio)/2, 10, 111][[1]] (* or *)
RealDigits[(5 - Sqrt[5])/4, 10, 111][[1]] (* Robert G. Wilson v, Jan 07 2018 *)

Prog

(PARI) (5-sqrt(5))/4 \\ Charles R Greathouse IV, Aug 31 2013

Crossrefs

Cf. A001622, A081011, A187426, A226765, A094874, A344212.

Sequence in context: A199451 A135154 A285832 * A371321 A339802 A257871

Adjacent sequences: A187795 A187796 A187797 * A187799 A187800 A187801

Keyword

nonn,cons

Author

Joost Gielen, Aug 30 2013

Extensions

Extended by Charles R Greathouse IV, Aug 31 2013

Status

approved