Comment problem in A005574

franktaw at netscape.net franktaw at netscape.net
Thu Oct 5 23:23:53 CEST 2006


In http://www.research.att.com/~njas/sequences/A005574,
"Numbers n such that n^2 + 1 is prime.", there is a comment
"Also integer part and half of the quotient in the continued
fraction expansion of sqrt(p), when the cycle length=1 ...".

The problem with this comment is that this continued fraction
property has nothing to do with n^2 + 1 being prime.  This is
the continued fraction expansion for sqrt(n^2 + 1) for any n.

My first reaction is that this comment ought to be removed,
and a crossref to A002522 (n^2 + 1) added instead.  There is
a comment in A002522 about the continued fraction,
although it isn't quite as clear as I would like: "The continued
fraction expansion of sqrt(a(n))-n is (2n,2n,2n,..........)." - not
standard notation.

What do people think?  Should there be a change here, or
just leave it as it is?  If something should change, what?

Franklin T. Adams-Watters

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