Mutliplicative continued fractions
Mitchell Harris
harris at tcs.inf.tu-dresden.de
Fri Jun 10 14:04:08 CEST 2005
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
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