Comment problem in A005574

Joseph Biberstine jrbibers at indiana.edu
Fri Oct 6 03:44:56 CEST 2006


My vote:
- Axe the comment in A5574 and replace with some ref to A2522.

- Edit the comment in A2522 to:
	"As the positive solution to x=2n+1/x is x=n+sqrt(a(n)), the continued
fraction expansion of sqrt(a(n)) is {n; {2n}}."

Is this notation (for terminal repetition in continued fraction
expansion representations) as common as I think?

franktaw at netscape.net wrote:
> 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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