Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

1,2

Also the limiting ratio of Lucas[n]/Fibonacci[n+1], or Fibonacci[n-1]/Fibonacci[n+1] + 1. - Alexander Adamchuk, Oct 10 2007

Ivan Panchenko, Table of n, a(n) for n = 1..1000

Paul Cooijmans, Odds.

J. Sondow, Evaluation of Tachiya's algebraic infinite products involving Fibonacci and Lucas numbers, Diophantine Analysis and Related Fields 2011 - AIP Conference Proceedings, vol. 1385, pp. 97-100.

(2-phi)*(2+phi) = 2 - 1/phi = 3-phi = (5-sqrt(5))/2 = (2*sin(Pi/5))^2, where phi is the golden ratio (A001622).

Equals prod(n>0, (1 + 1/A192223(n))). [Charles R Greathouse IV, Jun 26 2011]

1.38196601125010515179541316563436188...

(PARI) (5-sqrt(5))/2 \\ Charles R Greathouse IV, Jun 26 2011

Equals A079585-1.

Cf. A000032, A000045, A192223.

Sequence in context: A016622 A143623 * A132338 A132702 A197725 A022833

Adjacent sequences: A094871 A094872 A094873 * A094875 A094876 A094877

cons,nonn,easy

N. J. A. Sloane, Jun 14 2004

approved