Comment problem in A005574

[Richard Mathar]

ftaw> From seqfan-owner at ext.jussieu.fr  Thu Oct  5 23:24:50 2006
ftaw> Return-Path: <seqfan-owner at ext.jussieu.fr>
ftaw> Subject: Comment problem in A005574
ftaw> Date: Thu, 05 Oct 2006 17:23:53 -0400
ftaw> From: franktaw at netscape.net
ftaw> ...
ftaw> and a crossref to A002522 (n^2 + 1) added instead.  There is
ftaw> a comment in A002522 about the continued fraction,
ftaw> although it isn't quite as clear as I would like: "The continued
ftaw> fraction expansion of sqrt(a(n))-n is (2n,2n,2n,..........)." - not
ftaw> standard notation.
ftaw> ....

I'd propose to stay as close as possible to the flattened notation with 
the vertical bars. The first version for normalized continued fractions looks
like
2n|2n|2n|...
To admit cases of other numbers/sequences with general numerator/denominator
combinations, a more explicit format like
a0+b0/|a1+b1/|a2+b2/|a3+
would probably be wiser, where b0=b1=b2 etc is just another special case.
A quasi-notation like
a0+(a1+b1/(a2+b2/(a3+...)))
which can be interpreted with a mere high-school experience in maths is the
least ambiguous one, and can also be used for the terminating continuous
fractions. This last one is the one I'd prefer.

An entry of that kind into the "Notation" section
of the http://www.research.att.com/~njas/sequences/FAQ.html would make sense

RJM