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,r], where r = (1 + sqrt(5))/2. Ordinary continued fraction, as given by Mathematica program shown below:
[2,9,1,3,1,1,3,9,1,3,1,1,3,9,1,3,1,1,3,...]
EXAMPLE
2.10223743613619156978932391078013510172414229422761...
MATHEMATICA
r=(1+5^(1/2))/2;
FromContinuedFraction[{r, r, r, r}]
FullSimplify[%]
N[%, 130]
RealDigits[%] (*A189962*)
ContinuedFraction[%%]
RealDigits[3 (1+3*Sqrt[5])/11, 10, 150][[1]] (* Harvey P. Dale, Sep 11 2023 *)
PROG
(PARI) 3*(1+3*sqrt(5))/11 \\ G. C. Greubel, Jan 13 2018
(Magma) 3*(1+3*Sqrt(5))/11 // G. C. Greubel, Jan 13 2018
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, May 02 2011
EXTENSIONS
Definition corrected by G. C. Greubel, Jan 13 2018
STATUS
approved