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... .

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

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

KEYWORD

cons,nonn

AUTHOR

Joost Gielen, Sep 29 2013

STATUS

approved