A229780 Decimal expansion of (3+sqrt(5))/10.

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

Offset

0,1

Comments

sqrt((3+sqrt(5))/10) = sqrt((phi^2)/5 = (5+sqrt(5))/10 = (3+sqrt(5))/10)+2/10 = 0.723606797... .

Essentially the same as A134972, A134945, A098317 and A002163. - R. J. Mathar, Sep 30 2013

Equals one tenth of the limit of (G(n+2)+G(n+1)+G(n-1)+G(n-2))/G(n), where G(n) is any nonzero sequence satisfying the recurrence G(n+1) = G(n) + G(n-1) including A000032 and A000045, as n --> infinity. - Richard R. Forberg, Nov 17 2014

3+sqrt(5) is the perimeter of a golden rectangle with a unit width. - Amiram Eldar, May 18 2021

Constant x such that x = sqrt(x) - 1/5. - Andrea Pinos, Jan 15 2024

Links

Table of n, a(n) for n=0..98.

Formula

(3+sqrt(5))/10 = (phi/sqrt(5))^2 = phi^2/5 where phi is the golden ratio.

Example

0.5236067977499...

Mathematica

RealDigits[GoldenRatio^2/5, 10, 120][[1]] (* Harvey P. Dale, Dec 02 2014 *)

Crossrefs

Cf. A094874, A187798.

Sequence in context: A237200 A021195 A019673 * A272031 A090183 A063572

Adjacent sequences: A229777 A229778 A229779 * A229781 A229782 A229783

Keyword

cons,nonn

Author

Joost Gielen, Sep 29 2013

Status

approved