Mutliplicative continued fractions

[Mitchell Harris]

On Fri, 10 Jun 2005, David Wilson wrote:

>Mitchell Harris noted that the continued fraction of sqrt(n) is 
>multiplicative for certain n (where the integer part of sqrt(n) is taken to 
>be a(0) and is ignored with regard to the multiplicativity of the sequence).
>
>This begs two questions:
>
>- For which n is sqrt(n) multiplicative as described above?

which would make a nice sequence...starting:

   3, 7, 8, 13, 14, 15, 22, 23, 24, 32, 33, 34, 35, 44,...

(of course omitting perfect squares, whose continued fraction sequences 
are (quite rightly) not in the OEIS.


>- When is a periodic sequence multiplicative?

first simple pass - a necessary but not sufficient condition: a(1) must 
be 1, so any sqrt between x and x+1/2

-- 
Mitch Harris