[seqfan] Re: continued fraction offsets
Kevin Ryde
user42 at zip.com.au
Tue Jan 3 22:54:58 CET 2012
franktaw at netscape.net writes:
>
> No. I believe that 0 is the preferred offset for continued fractions.
A particularly curious set I noticed was the block
A010171 sqrt 103
A010172 sqrt 106
A010173 sqrt 107
A010174 sqrt 108
A010175 sqrt 109
which is in the middle of sqrts to 199 but this block has offset=1 where
all the others are offset=0. Dunno if it makes the "a(n)" formulas
shown easier or the same or different or something.
> There may be (not in your examples) some numbers between 0 and 1 that
> have continued fractions that do not have a leading zero and have
> offset 1, but the preferred form is to include a leading zero and make
> the offset be 0 (as for A002852).
Ah yeah. Though I notice A053002 1/AGM(1,sqrt(2))=0.83 is unlike that
as yet, offset=1 but starting with a leading 0 (and its B-file
likewise).
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