[seqfan] Re: A172074

[RGWv]

Frank,

    Except for the first term of 161 instead of 111, the sequence matches 
the CF of the Sqrt(12500). What was given was the CF of 100(1+Sqrt(5))/2 or 
simply 100 Phi. I can only speculate, but what I think the author was trying 
to show was that the CF of Sqrt(12500) has the same periodic as Phi.

Bob.

-----Original Message----- 
From: franktaw at netscape.net
Sent: Friday, September 09, 2011 10:01 PM
To: seqfan at seqfan.eu
Subject: [seqfan] A172074

https://oeis.org/A172074 (Continued fraction to calculate digits of the
golden ratio.)

I can't read Mathematica well enough to figure out what number this is
the continued fraction for. (It isn't sqrt(12500).)

Second, how does this relate to the golden ratio? There is no
explanation or reference. (It appears the number approximates 100*phi,
but there's still no detail - how accurate (actually equal?), how is
the sequence of approximations derived, etc. etc.)

Franklin T. Adams-Watters

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