Astronomical ratio, convention for continued fractions

[Richard Guy]

Compare The Book of Numbers, p.177.

Should it be 13 or 12 ????    R.

On Wed, 7 Jun 2006, Andrew Plewe wrote:

> I was reading about the Antikythera Mechanism at The Register:
>
> http://www.theregister.co.uk/2006/06/07/antikythera_mechanism/
>
> and while doing further Googling came across this AMS article detailing a
> continued fraction for computing the Astronomical ratio:
>
> http://www.ams.org/featurecolumn/archive/kyth3.html
>
>
> 13.368267..  = [13, 2, 1, 2, 1, 1, 17, ...]
>
>                   1
>           = 13 + ------------------------
>                      1
>                  2+ ---------------------
>                         1
>                     1+ ------------------
>                            1
>                        2+ ---------------
>                               1
>                           1+ ------------
>                                   1
>                               1+ --------
>                                       1
>                                  17+ ----
>                                       etc
>
> Anyway, I thought this might be of general interest to the list and worth
> adding to the OEIS if it isn't already in there. Would it be best to submit
> this as a decimal expansion, with the continued fraction listed in the
> comments or formula section? I see that the decimal expansion and continued
> fractions are listed as seperate sequences for the constant Pi but I'm not
> sure if people generally hold to this convention. Thanks!
>
> 	-Andrew Plewe-
>
>