OFFSET
1,1
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
FORMULA
Continued fraction (as explained at A188635): [r,r,r], where r = (1 + sqrt(5))/2. Ordinary continued fraction, as given by Mathematica program shown below:
[2,15,3,15,3,15,3,15,3,...]
From Amiram Eldar, Feb 06 2022: (Start)
Equals phi^4/sqrt(5) - 1, where phi is the golden ratio (A001622).
Equals lim_{k->oo} Fibonacci(k+4)/Lucas(k) - 1. (End)
MATHEMATICA
r=(1+5^(1/2))/2;
FromContinuedFraction[{r, r, r}]
FullSimplify[%]
N[%, 130]
RealDigits[%] (* A189961 *)
ContinuedFraction[%%]
RealDigits[(5+7*Sqrt[5])/10, 10, 150][[1]] (* Harvey P. Dale, Mar 30 2024 *)
PROG
(PARI) (5+7*sqrt(5))/10 \\ G. C. Greubel, Jan 13 2018
(Magma) (5+7*Sqrt(5))/10 // G. C. Greubel, Jan 13 2018
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, May 02 2011
STATUS
approved