Astronomical ratio, convention for continued fractions

[franktaw at netscape.net]

For important numbers, Neil likes to have both the decimal expansion 
and the continued fraction as separate sequences.  On the whole, there 
are a lot more decimal expansions in the database than continued 
fractions.

In a case like this, where the continued fraction has been published, I 
would say definitely add both.  Be sure to include the reference.

Franklin T. Adams-Watters


-----Original Message-----
From: Andrew Plewe <aplewe at sbcglobal.net>

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-



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